diff --git a/lib/lexers/lexNumber.ts b/lib/lexers/lexNumber.ts
index 2b04dae..b4490a6 100644
--- a/lib/lexers/lexNumber.ts
+++ b/lib/lexers/lexNumber.ts
@@ -6,34 +6,35 @@ const COLON = 58; // :
 
 function advDigits (str: string, pos: number): number {
   const start = pos;
-  do {
+  while (pos < str.length) {
     const c = str.charCodeAt(pos);
     if (c < 48 || c > 57) { // 0-9
       break;
     }
     pos++;
   }
-  while (pos < str.length);
   return pos - start;
 }
 
-// \d+(\.\d+)?(?:[eE][+-]?\d+)?
+// (?:\d+(\.\d*)?|\.\d+)(?:[eE][+-]?\d+)?
 export function lexNumber (str: string, pos: number): Token | undefined {
   const start = pos;
 
-  // integer
+  // integer part, optional when there is a fraction part (.5)
   const lead = advDigits(str, pos);
-  if (!lead) { return; }
   pos += lead;
 
-  // optional fraction part
+  // fraction part, optional when there is an integer part (5.)
   const c0 = str.charCodeAt(pos);
+  let frac = 0;
   if (c0 === 46) { // .
     pos++;
-    const frac = advDigits(str, pos);
-    if (!frac) { return; }
+    frac = advDigits(str, pos);
     pos += frac;
   }
+  if (!frac && !lead) {
+    return;
+  }
   // optional exponent part
   const c1 = str.charCodeAt(pos);
   if (c1 === 69 || c1 === 101) { // E e
diff --git a/lib/tokenize.spec.ts b/lib/tokenize.spec.ts
index 7b24adb..bd825c3 100644
--- a/lib/tokenize.spec.ts
+++ b/lib/tokenize.spec.ts
@@ -511,6 +511,94 @@ describe('lexer', () => {
       ]);
     });
 
+    test('decimals with no integer part', () => {
+      isTokens('=.5', [
+        { type: FX_PREFIX, value: '=' },
+        { type: NUMBER, value: '.5' }
+      ]);
+      isTokens('=A1*.95', [
+        { type: FX_PREFIX, value: '=' },
+        { type: REF_RANGE, value: 'A1' },
+        { type: OPERATOR, value: '*' },
+        { type: NUMBER, value: '.95' }
+      ]);
+      isTokens('=.5E-1', [
+        { type: FX_PREFIX, value: '=' },
+        { type: NUMBER, value: '.5E-1' }
+      ]);
+      isTokensNeg('=-.5', [
+        { type: FX_PREFIX, value: '=' },
+        { type: NUMBER, value: '-.5' }
+      ]);
+      // unary minus after a binary operator
+      isTokensNeg('=A1*-.95', [
+        { type: FX_PREFIX, value: '=' },
+        { type: REF_RANGE, value: 'A1' },
+        { type: OPERATOR, value: '*' },
+        { type: NUMBER, value: '-.95' }
+      ]);
+      isTokens('=A1*-.95', [
+        { type: FX_PREFIX, value: '=' },
+        { type: REF_RANGE, value: 'A1' },
+        { type: OPERATOR, value: '*' },
+        { type: OPERATOR, value: '-' },
+        { type: NUMBER, value: '.95' }
+      ]);
+      // a lone period is not a number
+      isTokens('=.', [
+        { type: FX_PREFIX, value: '=' },
+        { type: UNKNOWN, value: '.' }
+      ]);
+    });
+
+    test('a decimal with no integer part still yields to a following : or !', () => {
+      // the tail guard applies to the new form as to any number
+      for (const expr of [ '=.5:A1', '=.5!A1' ]) {
+        expect(tokenize(expr).filter(t => t.type === NUMBER)).toEqual([]);
+      }
+    });
+
+    test('decimals with no fraction part', () => {
+      isTokens('=1.*2', [
+        { type: FX_PREFIX, value: '=' },
+        { type: NUMBER, value: '1.' },
+        { type: OPERATOR, value: '*' },
+        { type: NUMBER, value: '2' }
+      ]);
+      isTokens('=(1.)', [
+        { type: FX_PREFIX, value: '=' },
+        { type: OPERATOR, value: '(' },
+        { type: NUMBER, value: '1.' },
+        { type: OPERATOR, value: ')' }
+      ]);
+      isTokens('=1.E5', [
+        { type: FX_PREFIX, value: '=' },
+        { type: NUMBER, value: '1.E5' }
+      ]);
+      isTokens('=1.e-2', [
+        { type: FX_PREFIX, value: '=' },
+        { type: NUMBER, value: '1.e-2' }
+      ]);
+      // Excel reads `=1.` as 1, at the end of the input like anywhere else
+      isTokens('=1.', [
+        { type: FX_PREFIX, value: '=' },
+        { type: NUMBER, value: '1.' }
+      ]);
+    });
+
+    test('dangling exponents are not numbers', () => {
+      // Excel refuses `=1E` and `=1.5e+` at entry
+      isTokens('=1E', [
+        { type: FX_PREFIX, value: '=' },
+        { type: UNKNOWN, value: '1E' }
+      ]);
+      isTokens('=1.5e+', [
+        { type: FX_PREFIX, value: '=' },
+        { type: UNKNOWN, value: '1.5e' },
+        { type: OPERATOR, value: '+' }
+      ]);
+    });
+
     test('scientific notation', () => {
       isTokens('=1E-1', [
         { type: FX_PREFIX, value: '=' },