Terminating decimals and fractions · Foundation
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| terminating decimal/ˈtɜːmɪneɪtɪŋ ˈdesɪml/ | 有限小数 | yǒu xiàn xiǎo shù |
Does the display tell the whole number?
- A calculator shows 0.333333. Is the display the exact value of one third, or only the digits that fit on the screen?
- This lesson studies terminating decimal 有限小数: A decimal that ends after a finite number of digits.
Choose the mathematical structure
- Use the place value of the last digit to write a power-of-ten denominator, then simplify. Compare numbers using matching decimal places or a common denominator.
- State the allowed inputs and units before calculating. An equation should express the relationship, not just record a calculator entry.
Which description correctly defines terminating decimal?
A decimal that ends after a finite number of digits.
Work through a checked case
- Check the result against the starting quantities. Substitute into the original relation, or compare the graph and numerical answer where appropriate.
0.375=375/1000=3/8. Also 3.5=35/10=7/2 and 0.06=6/100=3/50. To order 3/8 and 0.4, write 0.375 and 0.400; therefore 3/8<0.4.
Terminating decimals and fractions
Use the place value of the last digit to write a power-of-ten denominator, then simplify
Compare the model with the worked case and explain one change.
Find the numerator when 0.375 is expressed over 8.
375/1000 reduces to 3/8.
Test a tempting shortcut
- Keep the place value: 0.06 is six hundredths, not six tenths. A fraction may exceed 1. Simplify the entire numerator and denominator by the same common factor.
- When a shortcut fails, identify the assumption it breaks. Keep an exact value until the requested final rounding.
The finite decimal 0.375 equals 375/100. This claim is false. Explain which definition or assumption it violates.
Find the denominator of 3.5 in lowest terms.
35/10 reduces to 7/2, so the denominator is 2.
The finite decimal 0.375 equals 375/100.
Keep the place value: 0.06 is six hundredths, not six tenths. A fraction may exceed 1. Simplify the entire numerator and denominator by the same common factor.
Interpret a new situation
- AQA N10 Foundation covers terminating decimals and fractions, including ordering. Recurring-decimal conversion is reserved for the Higher lesson.
- A complete solution gives the mathematical result and explains what it means. Check that it is possible in the stated context.
Find the denominator of 0.06 in lowest terms.
6/100 reduces to 3/50, so the denominator is 50.
Match each part of a complete solution to its purpose.
An assumption justifies the model; a check tests the result; interpretation connects it to the question.
Use this in your course
- 8300 · Foundation · 3.1. Match the target tier and specification before assigning extensions.
- Give the method before the final answer, and use the paper's calculator and formula rules. Review a wrong answer by locating the first invalid step.
A decimal that ends after a finite number of digits. Choose the relationship, show the method, check its assumptions and interpret the result.