Rounding and estimation

We need to round 36.74 to 1 decimal place, which means we keep one digit after the decimal point.

To round to 1 d.p., look at the 2nd decimal place (hundredths digit). In 36.74, the hundredths digit is 4.

Since 4 is less than 5, we round down — we keep the tenths digit the same. The tenths digit is 7, so it stays as 7.

$36.74\approx 36.7°C$

We need to round 36.74 to 1 decimal place. The correct answer must have exactly one digit after the decimal point.

36.70°C has two decimal places written out, and keeping both digits unchanged does not represent a properly rounded answer to 1 d.p.

37.0°C would be the answer if we rounded to the nearest whole number, not to 1 decimal place. This is rounding too far.

36.8°C would require rounding the tenths digit up, which only happens when the hundredths digit is 5 or more. Here the hundredths digit is 4, so we do not round up.

36.7°C is correct because the hundredths digit (4) is less than 5, so we keep the tenths digit as 7.

When we round a number, the result is not exactly equal to the original — it is a nearby approximate value.

The symbol ≈ means approximately equal to. This is the correct symbol to use when writing rounded answers, for example: $63\approx 60$.

We use ≈ to show the answer is approximate, not exact. Writing = would incorrectly suggest the two values are identical.

We need to identify the symbol that shows a number has been rounded — meaning the value is approximate, not exact.

= means exactly equal to. Since rounding changes the value slightly, using = would be mathematically incorrect.

> means greater than. This is a comparison symbol and does not describe approximation.

≠ means not equal to. While a rounded number is indeed not exactly equal, this symbol does not communicate approximation.

≈ means approximately equal to and is the standard symbol used when expressing rounded values.