Another Peek Beyond the Point

Multiplying and dividing decimals, multiplying and dividing by 10, 100 and 1000, and writing fractions as decimals that end or repeat.

Key ideas

• To multiply decimals, multiply as whole numbers, then give the answer as many decimal places as the two numbers have together.
• Multiplying by 10, 100 or 1000 moves the digits 1, 2 or 3 places to the left (the point moves right); dividing moves them the other way.
• To divide by a decimal, multiply both numbers by 10, 100, … until the divisor is a whole number.
• To change a fraction to a decimal, divide the numerator by the denominator.
• In lowest terms, a fraction gives an ending decimal only if its denominator has no prime factors other than 2 and 5; otherwise the decimal repeats.

Remember

Watch out

• Counting decimal places from only one of the numbers when multiplying.
• Changing only the divisor, not both numbers, when dividing by a decimal.
• Thinking multiplying always makes a number bigger (× 0.5 halves it).

Worked example