diff --git a/Cargo.lock b/Cargo.lock
index ac62ebd..768d827 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -3904,7 +3904,7 @@ dependencies = [
 
 [[package]]
 name = "rcalc"
-version = "0.1.21"
+version = "0.1.25"
 dependencies = [
  "slint",
  "slint-build",
diff --git a/Cargo.toml b/Cargo.toml
index b55fb72..7c9e55d 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -1,6 +1,6 @@
 [package]
 name = "rcalc"
-version = "0.1.21"
+version = "0.1.25"
 edition = "2021"
 build = "build.rs"
 
diff --git a/dist/rcalc b/dist/rcalc
index 37d272e..71faa5c 100755
Binary files a/dist/rcalc and b/dist/rcalc differ
diff --git a/src/convert.rs b/src/convert.rs
index 8ef71c0..e43cfcb 100644
--- a/src/convert.rs
+++ b/src/convert.rs
@@ -391,7 +391,9 @@ impl Converter {
                 if !ch.is_ascii_hexdigit() {
                     return;
                 }
-                if self.draft == "0" {
+                // A synced all-zero draft ("0", "0000") is a placeholder:
+                // first digit replaces it instead of being swallowed.
+                if self.draft.chars().all(|c| c == '0') {
                     self.draft = ch.to_string();
                 } else if self.draft.len() < 4 {
                     self.draft.push(ch);
@@ -478,6 +480,11 @@ impl Converter {
                 if t.is_empty() || t == "-" || t == "." || t == "-." {
                     return Ok(());
                 }
+                // Exponent being typed: `1E`, `1E+`, `1E-` — intermediate
+                // state, keep the previous value without flagging an error.
+                if t.ends_with('E') || t.ends_with("E+") || t.ends_with("E-") {
+                    return Ok(());
+                }
                 match t.parse::<f32>() {
                     Ok(v) => {
                         self.float_bits = v.to_bits();
@@ -777,8 +784,20 @@ fn format_float(v: f32) -> String {
             "Inf".into()
         };
     }
-    let s = format!("{v}");
-    s
+    if v == 0.0 {
+        // Keep IEEE −0 visible (bits 0x8000_0000).
+        return if v.is_sign_negative() {
+            "-0".into()
+        } else {
+            "0".into()
+        };
+    }
+    // Scientific notation for extremes: keeps f32::MAX readable and the
+    // draft re-parsable (`3.4028235e38`.parse::<f32>() works).
+    if v.abs() < 1e-10 || v.abs() >= 1e16 {
+        return format!("{v:e}");
+    }
+    format!("{v}")
 }
 
 /// IEEE float bytes in natural order A B C D (big-endian bit pattern),
@@ -889,4 +908,71 @@ mod tests {
         assert_eq!(c.ascii_code(), b'A');
         assert_eq!(c.ascii_char_text(), "A");
     }
+
+    #[test]
+    fn float_draft_exponent_in_progress() {
+        // Typing `1E` is an intermediate state, not an error.
+        let mut c = Converter::new();
+        c.clear_active(); // draft "0"
+        c.input_char('1');
+        c.input_char('E');
+        assert_eq!(c.error(), None, "typing `1E` must not flag invalid float");
+        c.input_char('5');
+        assert_eq!(c.error(), None);
+        assert_eq!(c.float_value(), 1e5);
+    }
+
+    #[test]
+    fn float_draft_exponent_sign_in_progress() {
+        let mut c = Converter::new();
+        c.clear_active(); // draft "0"
+        c.input_char('1');
+        c.input_char('E');
+        c.input_char('-');
+        assert_eq!(c.error(), None, "typing `1E-` must not flag invalid float");
+        c.input_char('9');
+        assert_eq!(c.error(), None);
+        assert_eq!(c.float_value(), 1e-9);
+    }
+
+    #[test]
+    fn negative_zero_words() {
+        // IEEE -0.0 must round-trip through the word view (0x8000 0000).
+        let mut c = Converter::new();
+        c.clear_active(); // draft "0", float +0
+        c.input_char('-');
+        c.input_char('0');
+        assert_eq!(c.words(), (0x8000, 0x0000));
+        assert_eq!(c.float_text(), "-0");
+    }
+
+    #[test]
+    fn word_edit_updates_float() {
+        let mut c = Converter::new();
+        c.clear_active(); // float = 0
+        c.set_active(ConvField::Word0);
+        for ch in "3F80".chars() {
+            c.input_char(ch);
+        }
+        assert_eq!(c.float_value(), 1.0);
+    }
+
+    #[test]
+    fn huge_float_uses_scientific() {
+        // f32::MAX plain-decimal display is 39 chars; exponent form is
+        // readable and re-parsable by the float draft parser.
+        let t = format_float(f32::MAX);
+        assert!(t.contains('e'), "expected scientific notation, got {t}");
+        assert_eq!(t.parse::<f32>().unwrap(), f32::MAX);
+
+        let t = format_float(1e-20);
+        assert!(t.contains('e'), "expected scientific notation, got {t}");
+        assert_eq!(t.parse::<f32>().unwrap(), 1e-20);
+    }
+
+    #[test]
+    fn negative_zero_displayed() {
+        assert_eq!(format_float(-0.0), "-0");
+        assert_eq!(format_float(0.0), "0");
+    }
 }
diff --git a/src/engine.rs b/src/engine.rs
index 3bb3b39..fde8dce 100644
--- a/src/engine.rs
+++ b/src/engine.rs
@@ -77,18 +77,27 @@ impl Rational {
         Self { num: n, den: 1 }
     }
 
-    /// Parse a decimal literal like `12`, `-3.5`, `0.001` into an exact fraction.
+    /// Parse a decimal literal like `12`, `-3.5`, `0.001`, `1.5e-9` into an
+    /// exact fraction (exponent shifts by exact powers of ten).
     fn parse(s: &str) -> Result<Self, CalcError> {
         let s = s.trim();
         if s.is_empty() || s == "." || s == "-" || s == "-." {
             return Err(CalcError::Invalid);
         }
-        let neg = s.starts_with('-');
-        let body = if neg { &s[1..] } else { s };
+        // Split off an optional exponent: `1e-15`, `2.5E+3`.
+        let (body, exp) = match s.split_once(['e', 'E']) {
+            Some((b, e)) => {
+                let exp: i32 = e.parse().map_err(|_| CalcError::Invalid)?;
+                (b, exp)
+            }
+            None => (s, 0i32),
+        };
+        let neg = body.starts_with('-');
+        let b = if neg { &body[1..] } else { body };
 
-        let (int_part, frac_part) = match body.split_once('.') {
-            Some((a, b)) => (a, b),
-            None => (body, ""),
+        let (int_part, frac_part) = match b.split_once('.') {
+            Some((a, c)) => (a, c),
+            None => (b, ""),
         };
         if int_part.is_empty() && frac_part.is_empty() {
             return Err(CalcError::Invalid);
@@ -107,6 +116,27 @@ impl Rational {
             .and_then(|v| v.checked_add(frac_val))
             .ok_or(CalcError::Overflow)?;
         let num = if neg { -num } else { num };
+
+        // Apply the exponent with exact power-of-ten arithmetic:
+        // value·10^exp = num·10^exp / 10^frac_digits.
+        let (num, den) = if exp >= 0 {
+            let e = exp as usize;
+            if e >= frac_digits {
+                (
+                    num.checked_mul(pow10(e - frac_digits)?)
+                        .ok_or(CalcError::Overflow)?,
+                    1,
+                )
+            } else {
+                (num, den / pow10(e)?)
+            }
+        } else {
+            (
+                num,
+                den.checked_mul(pow10((-exp) as usize)?)
+                    .ok_or(CalcError::Overflow)?,
+            )
+        };
         Self::new(num, den)
     }
 
@@ -175,9 +205,14 @@ impl Value {
         if !v.is_finite() {
             return Err(CalcError::Overflow);
         }
-        // Prefer exact integer when float is (almost) integral.
-        if v.fract().abs() < 1e-12 && v.abs() < 1e15 {
-            return Ok(Value::Rat(Rational::from_i128(v.round() as i128)));
+        if v == 0.0 {
+            return Ok(Value::Rat(Rational::from_i128(0)));
+        }
+        // Prefer exact integer when float is (almost) integral. Never snap a
+        // sub-unit magnitude to an integer: that turned 1e-16 into `0`.
+        let r = v.round();
+        if r != 0.0 && (v - r).abs() < 1e-12 && v.abs() < 1e15 {
+            return Ok(Value::Rat(Rational::from_i128(r as i128)));
         }
         Ok(Value::Float(v))
     }
@@ -394,7 +429,7 @@ impl Calculator {
             self.entry = d.to_string();
         } else if self.entry == "-0" {
             self.entry = format!("-{d}");
-        } else if digit_count(&self.entry) < 16 {
+        } else if digit_count(&self.entry) < 40 && significant_digits(&self.entry) < 16 {
             self.entry.push(d);
         }
         self.entry_value = None;
@@ -911,6 +946,19 @@ fn tokenize(src: &str) -> Result<Vec<(Tok, Option<Value>)>, CalcError> {
                 while i < chars.len() && (chars[i].is_ascii_digit() || chars[i] == '.') {
                     i += 1;
                 }
+                // Optional decimal exponent: `1e-9`, `2.5E+3`.
+                if i < chars.len() && (chars[i] == 'e' || chars[i] == 'E') {
+                    let mut j = i + 1;
+                    if j < chars.len() && (chars[j] == '+' || chars[j] == '-') {
+                        j += 1;
+                    }
+                    if j < chars.len() && chars[j].is_ascii_digit() {
+                        i = j;
+                        while i < chars.len() && chars[i].is_ascii_digit() {
+                            i += 1;
+                        }
+                    }
+                }
                 let lit: String = chars[start..i].iter().collect();
                 let v = Value::from_entry(&lit)?;
                 out.push((Tok::Num, Some(v)));
@@ -984,6 +1032,15 @@ fn digit_count(s: &str) -> usize {
     s.chars().filter(|c| c.is_ascii_digit()).count()
 }
 
+/// Significant digits (leading zeros don't count) — caps precision, not
+/// magnitude, so `0.0000000000000001` (1e-16) can be typed.
+fn significant_digits(s: &str) -> usize {
+    s.chars()
+        .filter(|c| c.is_ascii_digit())
+        .skip_while(|&c| c == '0')
+        .count()
+}
+
 fn gcd(mut a: u128, mut b: u128) -> u128 {
     while b != 0 {
         let t = b;
@@ -1016,36 +1073,36 @@ fn format_rational(r: Rational) -> String {
 }
 
 fn terminating_decimal(r: Rational) -> Option<String> {
+    // Terminating iff den = 2^a · 5^b. Digit count after the point is
+    // k = max(a, b); scale num so the denominator becomes exactly 10^k.
     let mut den = r.den;
+    let (mut a, mut b) = (0u32, 0u32);
     while den % 2 == 0 {
         den /= 2;
+        a += 1;
     }
     while den % 5 == 0 {
         den /= 5;
+        b += 1;
     }
     if den != 1 {
         return None;
     }
-    // Scale denominator to a power of 10.
-    let mut d = r.den;
-    let mut n = r.num;
-    let neg = n < 0;
-    n = n.abs();
-    while d % 10 != 0 {
-        if d % 2 == 0 {
-            d *= 5;
-            n *= 5;
-        } else if d % 5 == 0 {
-            d *= 2;
-            n *= 2;
-        } else {
-            break;
-        }
+    let k = a.max(b);
+    let mut n = r.num.abs();
+    for _ in 0..(k - a) {
+        n = n.checked_mul(2)?;
+    }
+    for _ in 0..(k - b) {
+        n = n.checked_mul(5)?;
+    }
+    let mut d: i128 = 1;
+    for _ in 0..k {
+        d = d.checked_mul(10)?;
     }
     let int_part = n / d;
     let mut frac = (n % d).to_string();
-    let width = d.to_string().len().saturating_sub(1);
-    while frac.len() < width {
+    while frac.len() < k as usize {
         frac.insert(0, '0');
     }
     // trim trailing zeros
@@ -1057,24 +1114,26 @@ fn terminating_decimal(r: Rational) -> Option<String> {
     } else {
         format!("{int_part}.{frac}")
     };
-    Some(if neg { format!("-{body}") } else { body })
+    Some(if r.num < 0 { format!("-{body}") } else { body })
 }
 
 fn format_float(v: f64) -> String {
-    if !v.is_finite() {
+    if !v.is_finite() || v == 0.0 {
         return "0".into();
     }
-    // Snap near-integers (guards any float path residue).
-    if (v - v.round()).abs() < 1e-10 && v.abs() < 1e15 {
-        return format!("{}", v.round() as i64);
+    // Snap near-integers (guards any float path residue); never for |v| < 1,
+    // otherwise tiny results like 1e-16 collapse to `0`.
+    let r = v.round();
+    if r != 0.0 && (v - r).abs() < 1e-10 && v.abs() < 1e15 {
+        return format!("{}", r as i64);
     }
-    let s = format!("{:.12}", v);
-    let s = s.trim_end_matches('0').trim_end_matches('.').to_string();
-    if s.is_empty() || s == "-" {
-        "0".into()
-    } else {
-        s
+    // Very small / large magnitudes: scientific notation keeps the value
+    // visible and re-parseable (`Rational::parse` understands exponents).
+    if v.abs() < 1e-10 || v.abs() >= 1e16 {
+        return format!("{v:e}");
     }
+    // Shortest representation that round-trips back to `v` exactly.
+    format!("{v}")
 }
 
 impl fmt::Display for Rational {
@@ -1173,4 +1232,107 @@ mod tests {
         let r = Rational::parse("1.25").unwrap();
         assert_eq!(r, Rational::new(5, 4).unwrap());
     }
+
+    // --- regression tests (rounding / formatting bugs) ---
+
+    #[test]
+    fn quarter_and_eighth_display() {
+        // terminating_decimal scaled the fraction wrong: 1/4 displayed as "0.5".
+        let mut c = Calculator::new();
+        c.input_digit('1');
+        c.set_op(Op::Div);
+        c.input_digit('4');
+        c.equals();
+        assert_eq!(c.display(), "0.25");
+
+        c.clear_all();
+        c.input_digit('1');
+        c.set_op(Op::Div);
+        c.input_digit('8');
+        c.equals();
+        assert_eq!(c.display(), "0.125");
+    }
+
+    #[test]
+    fn five_hundredths_display() {
+        // 0.05 must survive exact formatting (was displayed as "0.1").
+        let mut c = Calculator::new();
+        c.input_digit('0');
+        c.input_dot();
+        c.input_digit('0');
+        c.input_digit('5'); // 0.05
+        c.set_op(Op::Mul);
+        c.input_digit('1');
+        c.equals();
+        assert_eq!(c.display(), "0.05");
+    }
+
+    #[test]
+    fn tiny_reciprocal_not_zero() {
+        // 1/9999999999999999 ≈ 1e-16 was snapped to "0" by format_float.
+        let mut c = Calculator::new();
+        for d in "9999999999999999".chars() {
+            c.input_digit(d);
+        }
+        c.reciprocal();
+        let disp = c.display();
+        assert!(disp != "0", "tiny reciprocal must not display as 0, got {disp}");
+    }
+
+    #[test]
+    fn tiny_result_reusable_standard() {
+        // Float result in scientific notation must be re-parsable as operand.
+        let mut c = Calculator::new();
+        for d in "9999999999999999".chars() {
+            c.input_digit(d);
+        }
+        c.reciprocal();
+        c.set_op(Op::Mul);
+        c.input_digit('2');
+        c.equals();
+        let disp = c.display();
+        assert!(disp != "0" && disp != "Invalid input", "got {disp}");
+    }
+
+    #[test]
+    fn sqrt_square_roundtrip_tiny() {
+        // √(1e-30) = 1e-15 was snapped to 0 by Value::from_f64.
+        let mut c = Calculator::new();
+        c.input_dot(); // "0."
+        for _ in 0..14 {
+            c.input_digit('0');
+        }
+        c.input_digit('1'); // 0.000000000000001 = 1e-15
+        c.square();
+        c.sqrt();
+        let disp = c.display();
+        assert!(disp != "0", "sqrt(1e-30) must not display as 0, got {disp}");
+    }
+
+    #[test]
+    fn rational_parse_exponent() {
+        // Scientific-notation entries must parse to exact fractions.
+        let r = Rational::parse("1e-15").unwrap();
+        assert_eq!(r, Rational::new(1, 1_000_000_000_000_000).unwrap());
+        let r = Rational::parse("1.5e3").unwrap();
+        assert_eq!(r, Rational::new(1500, 1).unwrap());
+        let r = Rational::parse("2.5e-2").unwrap();
+        assert_eq!(r, Rational::new(1, 40).unwrap());
+        let r = Rational::parse("-1E+3").unwrap();
+        assert_eq!(r, Rational::new(-1000, 1).unwrap());
+        assert!(Rational::parse("1e2e3").is_err());
+        assert!(Rational::parse("1e").is_err());
+    }
+
+    #[test]
+    fn can_type_one_e_minus_16() {
+        // Leading zeros must not eat the 16-significant-digit budget.
+        let mut c = Calculator::new();
+        c.input_dot();
+        for _ in 0..15 {
+            c.input_digit('0');
+        }
+        c.input_digit('1');
+        assert_eq!(c.display(), "0.0000000000000001");
+    }
 }
diff --git a/src/engineering.rs b/src/engineering.rs
index 2925e11..680e5ce 100644
--- a/src/engineering.rs
+++ b/src/engineering.rs
@@ -199,7 +199,7 @@ impl Engineering {
             self.entry = d.to_string();
         } else if self.entry == "-0" {
             self.entry = format!("-{d}");
-        } else if digit_count(&self.entry) < 16 {
+        } else if digit_count(&self.entry) < 40 && significant_digits(&self.entry) < 16 {
             self.entry.push(d);
         }
         self.sync_expr();
@@ -550,20 +550,31 @@ fn digit_count(s: &str) -> usize {
     s.chars().filter(|c| c.is_ascii_digit()).count()
 }
 
+/// Significant digits (leading zeros don't count) — caps precision, not
+/// magnitude, so `0.0000000000000001` (1e-16) can be typed.
+fn significant_digits(s: &str) -> usize {
+    s.chars()
+        .filter(|c| c.is_ascii_digit())
+        .skip_while(|&c| c == '0')
+        .count()
+}
+
 fn format_num(v: f64) -> String {
-    if !v.is_finite() {
+    if !v.is_finite() || v == 0.0 {
         return "0".into();
     }
-    if (v - v.round()).abs() < 1e-10 && v.abs() < 1e15 {
-        return format!("{}", v.round() as i64);
+    // Snap near-integers; never for |v| < 1 (kept 10^−50 displayed as "0").
+    let r = v.round();
+    if r != 0.0 && (v - r).abs() < 1e-10 && v.abs() < 1e15 {
+        return format!("{}", r as i64);
     }
-    let s = format!("{:.12}", v);
-    let s = s.trim_end_matches('0').trim_end_matches('.').to_string();
-    if s.is_empty() || s == "-" {
-        "0".into()
-    } else {
-        s
+    // Scientific notation for extremes; `entry.parse::<f64>()` and the
+    // tokenizer both accept it, so the result stays reusable.
+    if v.abs() < 1e-10 || v.abs() >= 1e16 {
+        return format!("{v:e}");
     }
+    // Shortest round-trip representation.
+    format!("{v}")
 }
 
 // --- expression evaluator ---
@@ -639,6 +650,20 @@ fn tokenize(src: &str) -> Result<Vec<Tok>, SciError> {
                 while i < chars.len() && (chars[i].is_ascii_digit() || chars[i] == '.') {
                     i += 1;
                 }
+                // Optional decimal exponent: `1e-9`, `2.5E+3`. The standalone
+                // constant `e` stays an Ident (needs no digit right after).
+                if i < chars.len() && (chars[i] == 'e' || chars[i] == 'E') {
+                    let mut j = i + 1;
+                    if j < chars.len() && (chars[j] == '+' || chars[j] == '-') {
+                        j += 1;
+                    }
+                    if j < chars.len() && chars[j].is_ascii_digit() {
+                        i = j;
+                        while i < chars.len() && chars[i].is_ascii_digit() {
+                            i += 1;
+                        }
+                    }
+                }
                 let lit: String = chars[start..i].iter().collect();
                 let v: f64 = lit.parse().map_err(|_| SciError::Invalid)?;
                 out.push(Tok::Num(v));
@@ -858,4 +883,50 @@ mod tests {
         e.equals();
         assert_eq!(e.display(), "1024");
     }
+
+    #[test]
+    fn ten_pow_negative_not_zero() {
+        // 10 ^ −50 ≈ 1e-50 was snapped to "0" by format_num.
+        let mut e = Engineering::new();
+        e.input_digit('1');
+        e.input_digit('0');
+        e.set_op("^");
+        e.input_digit('5');
+        e.input_digit('0');
+        e.negate();
+        e.equals();
+        let disp = e.display();
+        assert!(disp != "0", "10^−50 must not display as 0, got {disp}");
+    }
+
+    #[test]
+    fn tiny_float_result_continues_expression() {
+        // Result in scientific notation must be re-parsable by the tokenizer.
+        let mut e = Engineering::new();
+        e.input_digit('1');
+        e.input_digit('0');
+        e.set_op("^");
+        e.input_digit('1');
+        e.input_digit('6');
+        e.negate();
+        e.equals();
+        assert_eq!(e.display(), "1e-16");
+        e.set_op("+");
+        e.input_digit('1');
+        e.equals();
+        assert_eq!(e.display(), "1");
+    }
+
+    #[test]
+    fn can_type_one_e_minus_16() {
+        // Leading zeros must not eat the 16-significant-digit budget.
+        let mut e = Engineering::new();
+        e.input_digit('0');
+        e.input_dot();
+        for _ in 0..15 {
+            e.input_digit('0');
+        }
+        e.input_digit('1');
+        assert_eq!(e.display(), "0.0000000000000001");
+    }
 }
diff --git a/src/programmer.rs b/src/programmer.rs
index 3c5683e..da55603 100644
--- a/src/programmer.rs
+++ b/src/programmer.rs
@@ -699,4 +699,35 @@ mod tests {
         assert_eq!(p.word_size(), WordSize::Dint);
         assert_eq!(p.dec_text().replace(' ', ""), "-1");
     }
+
+    #[test]
+    fn shift_count_mods_word_size() {
+        // Locks hardware-style semantics: shift count is taken modulo the
+        // word size (1 << 100000000 → 1e8 % 64 == 0 → no shift).
+        let mut p = Programmer::new();
+        p.input_digit('1');
+        p.set_op(ProgOp::Lsh);
+        for ch in "100000000".chars() {
+            p.input_digit(ch);
+        }
+        p.equals();
+        assert_eq!(p.current_bits(), 1);
+    }
+
+    #[test]
+    fn shift_out_of_word_gives_zero() {
+        // 0xFFFF_FFFF_FFFF_FFFF Lsh 63 → only bit 0 survives at bit 63.
+        let mut p = Programmer::new();
+        p.set_base(Base::Hex);
+        for ch in "FFFFFFFFFFFFFFFF".chars() {
+            p.input_digit(ch);
+        }
+        p.set_op(ProgOp::Lsh);
+        p.set_base(Base::Dec); // type the shift count in decimal
+        p.input_digit('6');
+        p.input_digit('3');
+        p.equals();
+        // (u64::MAX << 63) & u64::MAX = 0x8000_0000_0000_0000
+        assert_eq!(p.current_bits(), 0x8000_0000_0000_0000);
+    }
 }