Rounding numbers

Rounding Numbers

  • Rounding is a mathematical process used to simplify numbers to a degree where they are suitable for practical use, but still accurate enough to be valuable.

  • When rounding numbers, you will typically be asked to round to the nearest whole number, or to a specific number of decimal places.

  • The general rule when rounding is that if the number you are rounding is followed by 5 or more, round up. If it’s less than 5, round down.

Rounding to the Nearest Whole Number

  • When rounding to the nearest whole number, look at the decimal place value directly after the decimal point: if it is 5 or more, you round up the number and if it is less than 5, you round down. For example, 7.6 rounds to 8, while 7.4 rounds to 7.

Rounding to a Specific Number of Decimal Places

  • To round to a specific number of decimal places, locate the correct digit then apply the general rounding rules. For example, to round 7.348 to 2 decimal places, you look at the third decimal place (the 8), which is more than 5, so you round up the second decimal place number from 4 to 5, giving 7.35.

Rounding Significant Figures

  • Significant figures refer to all the digits that carry meaning contributing to its precision.

  • To round to a specific number of significant figures, you identify the final significant digit required and then round up or down based on the next digit. For example, to round 7.348 to 2 significant figures, we look at the third digit (which is 4, less than 5) so we round down the second significant digit (which is 3) to remain as it is, giving 7.3.

Rounding in the Real World

  • The concept of rounding is frequently used in everyday situations where exact numbers aren’t necessary, such as estimating costs or measurements.

  • For example, if a meal costs £6.57, you might round this to £7 when budgeting or planning your finances.

  • Engineers, architects, carpenters, and other professions involving measurements often employ rounding to estimate needed resources or to assess project feasibility.

  • Understanding the principles behind rounding is crucial for higher level maths exams and mathematical applications beyond school in all areas of life.