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Class 7 Another Peek Beyond the Point: cheat sheet
CBSE Mathematics. 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
| Example | 0.3 × 0.04 = 0.012 (3 places in all) |
| Dividing | 1.44 ÷ 0.12 = 144 ÷ 12 = 12 |
| Fractions | 3/8 = 0.375 (ends); 2/3 = 0.666… (repeats) |
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
Write 14/15 as a decimal to 6 places. Does it end, or does it repeat?
Working: the remainders start to come round again, so the digits repeat
Answer: 0.933333…; it repeats
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