Rounding Numbers High School Math Topics Rounding Numbers

Rounding Numbers High School Math Topics Rounding Numbers Rounding to the Nearest 100 Rounding to a given number of Decimal Places Rounding to a given number of Significant Figures Number

Rounding Numbers Sometimes we may wish to round the answer to a calculation. There are different ways in which we can round numbers. These include: Rounding to the nearest 10, 100, etc. Rounding to a given number of Decimal Places. Rounding to a given number of Significant Figures. We will consider each of these methods. High School Math Topics - Number

Rounding to the Nearest 10 This means we write the nearest multiple of 10 to our number. Example 1: Round 38 to the nearest 10. Number Scale Multiple of 10 Our Number Our number is nearest to this value Multiple of 10 38 = 40 (to the nearest 10) High School Math Topics - Number 30 31 32 33 34 35 36 37 38 39 40

Rounding to the Nearest 10 This means we write the nearest multiple of 10 to our number. Example 2: Round 63 to the nearest 10. Our number is nearest to this value Number Scale Multiple of 10 Our Number Multiple of 10 63 = 60 (to the nearest 10) High School Math Topics - Number 60 61 62 63 64 65 66 67 68 69 70

Rounding to the Nearest 10 This means we write the nearest multiple of 10 to our number. Example 3: Round 75 to the nearest 10. Number Scale Multiple of 10 Our Number is Exactly Half Way If it’s exactly half way we round UP Our Number Multiple of 10 75 = 80 (to the nearest 10) High School Math Topics - Number 70 71 72 73 74 75 76 77 78 79 80

Rounding to the Nearest 10 This means we write the nearest multiple of 10 to our number. Example 4: Round 377 to the nearest 10. Number Scale Multiple of 10 Our Number Our number is nearest to this value Multiple of 10 377 = 380 (to the nearest 10) High School Math Topics - Number 370 371 372 373 374 375 376 377 378 379 380

Rounding to the Nearest 100 This means we write the nearest multiple of 100 to our number. Example 1: Round 263 to the nearest 100. Number Scale Multiple of 100 Our Number Our number is nearest to this value Multiple of 100 263 = 300 (to the nearest 100) High School Math Topics - Number 200 210 220 230 240 250 260 270 280 290 300

Rounding to the Nearest 100 This means we write the nearest multiple of 100 to our number. Example 2: Round 641 to the nearest 100. Our number is nearest to this value Number Scale Multiple of 100 Our Number Multiple of 100 641 = 600 (to the nearest 100) High School Math Topics - Number 600 610 620 630 640 650 660 670 680 690 700

Rounding to the Nearest 100 This means we write the nearest multiple of 100 to our number. Example 3: Round 350 to the nearest 100. Number Scale Multiple of 100 Our Number is Exactly Half Way If it’s exactly half way we round UP Our Number Multiple of 100 350 = 400 (to the nearest 100) High School Math Topics - Number 300 310 320 330 340 350 360 370 380 390 400

Rounding to a given number of Decimal Places The number of decimal places is the number of digits after the decimal point. Example 1: Round 8. 537 to two decimal places. This means that there has to be TWO digits after the decimal point in the answer. We look at the NEXT digit to decide whether or not to round up. If this digit is FIVE OR MORE we round up. 8. 537 So round this digit up by 1 to make it into a 4 8. 537 = 8. 54 (to 2 DP) High School Math Topics - Number This is 5 or over.

Rounding to a given number of Decimal Places The number of decimal places is the number of digits after the decimal point. Example 2: Round 16. 474 to two decimal places. This means that there has to be TWO digits after the decimal point in the answer. We look at the NEXT digit to decide whether or not to round up. If this digit is FIVE OR MORE we round up. 16. 474 So leave this digit as it is. 16. 474 = 16. 47 (to 2 DP) High School Math Topics - Number This is less than 5.

Rounding to a given number of Decimal Places The number of decimal places is the number of digits after the decimal point. Example 3: Round 8. 4613 to three decimal places. This means that there has to be THREE digits after the decimal point in the answer. We look at the NEXT digit to decide whether or not to round up. If this digit is FIVE OR MORE we round up. 8. 4613 So leave this digit as it is. 8. 4613 = 8. 461 (to 3 DP) High School Math Topics - Number This is less than 5.

Rounding to a given number of Decimal Places The number of decimal places is the number of digits after the decimal point. Example 4: Round 23. 51682 to three decimal places. This means that there has to be THREE digits after the decimal point in the answer. We look at the NEXT digit to decide whether or not to round up. If this digit is FIVE OR MORE we round up. 23. 51682 So round this digit up by 1 to make it into a This is 5 or over. 7 23. 51682 = 23. 517 (to 3 DP) High School Math Topics - Number

Rounding to a given number of Decimal Places The number of decimal places is the number of digits after the decimal point. Example 5: Round 0. 91356 to three decimal places. This means that there has to be THREE digits after the decimal point in the answer. We look at the NEXT digit to decide whether or not to round up. If this digit is FIVE OR MORE we round up. 0. 91356 So round this digit up by 1 to make it into a 4 0. 91356 = 0. 914 (to 3 DP) High School Math Topics - Number This is 5 or over.

Rounding to a given number of Decimal Places The number of decimal places is the number of digits after the decimal point. Example 6: Round 3. 42971 to three decimal places. This means that there has to be THREE digits after the decimal point in the answer. We look at the NEXT digit to decide whether or not to round up. If this digit is FIVE OR MORE we round up. 3. 42971 As this is a 9, we round the last two digits, (29) to 30 3. 42971 = 3. 430 (to 3 DP) High School Math Topics - Number This is 5 or over.

Rounding to a given number of Significant Figures The number of significant figures is the maximum number of non-zero digits in the rounded number. Example 1: Round 37642 to two significant figures. This means that there has to be a maximum of TWO non-zero digits. These are the first TWO SIGNIFICANT Figures We look at the NEXT digit. If this is FIVE OR MORE we round up. We replace other digits with zeros to keep the non-zero digits in the right place. 37642 So round this digit up by 1 to make it into an This is 5 or over. 8 38000 37642 = 38000 (to 2 SF) High School Math Topics - Number

Rounding to a given number of Significant Figures The number of significant figures is the maximum number of non-zero digits in the rounded number. Example 2: Round 7623 to two significant figures. This means that there has to be a maximum of TWO non-zero digits. These are the first TWO SIGNIFICANT Figures We look at the NEXT digit. If this is FIVE OR MORE we round up. We replace other digits with zeros to keep the non-zero digits in the right place. 7623 So leave this digit as it is. This is less than 5. 7600 7623 = 7600 (to 2 SF) High School Math Topics - Number

Rounding to a given number of Significant Figures The number of significant figures is the maximum number of non-zero digits in the rounded number. Example 3: Round 59681 to two significant figures. This means that there has to be a maximum of TWO non-zero digits. These are the first TWO SIGNIFICANT Figures We look at the NEXT digit. If this is FIVE OR MORE we round up. We replace other digits with zeros to keep the non-zero digits in the right place. 59681 As this is a 9, we round the last two digits, (59) to 60 This is 5 or over. 60000 59681 = 60000 (to 2 SF) High School Math Topics - Number

Rounding to a given number of Significant Figures The number of significant figures is the maximum number of non-zero digits in the rounded number. Example 4: Round 64089 to three significant figures. This means that there has to be a maximum of THREE non-zero digits. These are the first THREE SIGNIFICANT Figures We look at the NEXT digit. If this is FIVE OR MORE we round up. We replace other digits with zeros to keep the non-zero digits in the right place. 64089 So round this digit up by 1 to make it into an This is 5 or over. 1 64100 64089 = 64100 (to 3 SF) High School Math Topics - Number

Rounding to a given number of Significant Figures The number of significant figures is the maximum number of non-zero digits in the rounded number. Example 5: Round 1434 to three significant figures. This means that there has to be a maximum of THREE non-zero digits. These are the first THREE SIGNIFICANT Figures We look at the NEXT digit. If this is FIVE OR MORE we round up. We replace other digits with zeros to keep the non-zero digits in the right place. 1434 So leave this digit as it is. This is less than 5. 1430 1434 = 1430 (to 3 SF) High School Math Topics - Number

Rounding to a given number of Significant Figures The number of significant figures is the maximum number of non-zero digits in the rounded number. Example 6: Round 5. 276 to three significant figures. This means that there has to be a maximum of THREE non-zero digits. These are the first THREE SIGNIFICANT Figures We look at the NEXT digit. If this is FIVE OR MORE we round up. If the number is a decimal we don’t add zeros AFTER the decimal point. 5. 276 So round this digit up by 1 to make it into an 8 5. 276 = 5. 28 (to 3 SF) High School Math Topics - Number This is 5 or over.

Rounding to a given number of Significant Figures The number of significant figures is the maximum number of non-zero digits in the rounded number. Example 7: Round 3. 844 to three significant figures. This means that there has to be a maximum of THREE non-zero digits. These are the first THREE SIGNIFICANT Figures We look at the NEXT digit. If this is FIVE OR MORE we round up. If the number is a decimal we don’t add zeros AFTER the decimal point. 3. 844 So leave this digit as it is. This is less than 5. 3. 844 = 3. 84 (to 3 SF) High School Math Topics - Number

Rounding to a given number of Significant Figures The number of significant figures is the maximum number of non-zero digits in the rounded number. Example 8: Round 2647. 21 to three significant figures. This means that there has to be a maximum of THREE non-zero digits. These are the first THREE SIGNIFICANT Figures We look at the NEXT digit. If this is FIVE OR MORE we round up. If the number is a decimal we don’t add zeros AFTER the decimal point. 2647. 21 So round this digit up by 1 to make it into an This is 5 or over. 5 2650 2647. 21 = 2650 (to 3 SF) High School Math Topics - Number