GCSE Maths · Decimals, Rounding and Estimation · Higher · Summary

GCSE Maths Decimals, Rounding and Estimation (Higher): summary and key words

Part of the GCSE Maths decimals, rounding and estimation chapter (Higher). Chapter overview · Foundation version of this lesson · whole chapter on one page

Chapter summary

Skill	Method
Place value and ordering	Columns are worth 10 times the one on their right. Add zeros so decimals have the same number of places, then compare column by column.
× or ÷ by 10, 100, 1000	Move the digits 1, 2, 3 places left (×) or right (÷). The decimal point does not move.
Add and subtract decimals	Decimal points in a vertical line, fill gaps with zeros, work from the right, carry or exchange.
Multiply decimals	Count total decimal places, multiply as whole numbers, put the point back so the answer has that many decimal places.
Divide decimals	Make the divisor a whole number (multiply both numbers by 10, 100…), then short division with the point kept in line.
Decimal ↔ fraction	Last decimal place gives the denominator (10, 100, 1000); simplify. Fraction to decimal: top ÷ bottom or make the denominator 10, 100, 1000.
Rounding to d.p. and s.f.	Find the last digit to keep, look at the decider (5 or more rounds up). Significant figures start at the first non-zero digit. Use placeholder zeros for big numbers.
Truncation	Cut off after the chosen digit without rounding.
Estimation	Round every number to 1 s.f., follow BIDMAS, compare with the exact answer to check it. Never round a number to 0.
Error intervals	Rounding: value ± half a unit, written lower ≤ x < upper. Truncation: value ≤ x < value + one unit.
Bounds in calculations (Higher)	Sum and product use matching bounds. For a − b: UB_a − LB_b. For a ÷ b: UB_a ÷ LB_b. Then round both bounds to find a suitable accuracy.

I can read, write, compare and order decimals using place value.
I can multiply and divide by 10, 100 and 1000.
I can add and subtract decimals using column methods.
I can multiply decimals by counting decimal places.
I can divide by whole numbers and by decimals.
I can convert between terminating decimals and fractions.
I can round to a given number of decimal places or significant figures.
I can truncate a number.
I can estimate an answer by rounding to 1 significant figure and use it to check a calculation.
I can write an error interval for a rounded or truncated number.
(Higher) I can find the upper and lower bounds of a calculation and give the answer to a suitable accuracy.

Decimal place: A digit after the decimal point.
Place value: The value a digit has because of the column it is in.
Placeholder zero: A zero used to keep the other digits in the correct columns.
Terminating decimal: A decimal that stops after a fixed number of digits, such as 0.375.
Round: To replace a number by a nearby number that is easier to use.
Decider: The digit just after the last digit you keep when rounding.
Significant figure: A digit that counts towards the accuracy of a number, counted from the first non-zero digit.
Truncate: To cut off a number after a chosen digit without rounding.
Estimate: An approximate answer found with simple numbers, usually by rounding to 1 significant figure.
Error interval: The range of values a number could have had before it was rounded or truncated.
Lower bound: The smallest value that rounds to a given number.
Upper bound: The value at the top of the error interval; the least number that would round up to the next value.
Limits of accuracy: The lower and upper bounds of a measurement or calculation.
Inequality: A statement using <, >, ≤ or ≥, such as 3.35 ≤ x < 3.45.