Decimal Fractions

329.85

Step 1: When multiplying a decimal by 100, we shift the decimal point to the RIGHT by 2 places (because 100 has 2 zeros). Step 2: 3.2985 → shift decimal 2 places right → 329.85. Step 3: Verify: 3.2985 × 100 = 329.85. A common mistake is shifting in the wrong direction. Remember: multiply = shift right, divide = shift left.

62.342

Step 1: When dividing a decimal by 10, we shift the decimal point to the LEFT by 1 place (because 10 has 1 zero). Step 2: 623.42 → shift decimal 1 place left → 62.342. Step 3: Verify: 62.342 × 10 = 623.42 ✓. Remember the rule: dividing by 10 shifts decimal left by 1, by 100 shifts left by 2, and so on.

5.375

Step 1: We need to convert 3/8 to a decimal. Divide 3 by 8. Step 2: 3.000 ÷ 8: 8 goes into 30 three times (3×8=24), remainder 6. 8 goes into 60 seven times (7×8=56), remainder 4. 8 goes into 40 five times (5×8=40), remainder 0. Step 3: So 3/8 = 0.375. Step 4: Therefore 5 and 3/8 = 5 + 0.375 = 5.375. This is a terminating decimal because division ends with remainder 0.

4

Step 1: Count the number of digits after the decimal point in 0.5497. Step 2: After the decimal point we have: 5, 4, 9, 7 — that is 4 digits. Step 3: Therefore, 0.5497 has 4 decimal places. Remember: decimal places = number of digits written after the decimal point, regardless of whether they are zeros or not.