# Approximate Values

In this type of questions, candidates do not have to find out the exact value but approximate value after rounding off numbers. An approximate answer can be found more quickly. Rounding off a number to a decimal place means finding the multiple of the representative of that decimal place which is closest to the original number.

Thus, rounding off a number to the nearest hundred means finding the multiple of a 100 which is closest to the original number. Rounding off to the nearest tenth means finding the multiple of 1/10 which is closest to the original number.

After a number has been rounded off to a particular decimal place, all the digits to the right of that particular decimal place will be zero.

** Example :** Round off 7, 309, 310 to the nearest hundred.

** Solution :** You must find the multiple of the hundred which is closest to the 7,309,310

The answer is 7,309.300

To round a number to the nearest ten consider the ones digit. If the ones digit is 5 or greater than 5, then change the ten digit to the next higher digit and ones digit to zero. If the one digit is less then 5, then leave the tens digit unchanged but change the ones digit to zero.

To round a number to the nearest hundred, consider the tens digit. If the tens digit is 5 or greater than 5, then change the hundreds digits to zeros. If the ten digit is less than 5, then leave the hundreds digit unchanged but change the tens and ones digits to zeros.

To round a number to the nearest thousand, consider the hundreds digit. If the digit is 5 or greater than 5, then change the thousands digits to the next higher digit and change all the other digits before that to zeros. If the hundreds digits is less than 5, then leave the thousands digits unchanged but change all the other digits before that to zeros.

**Study the following**

Number | Round to the nearest | Digit to be Considered |
---|---|---|

395 | ten | 5 |

625 | hundred | 2 |

875623 | thousand | 6 |

531924 | ten-thousand | 1 |

472804 | lakh | 7 |

**Example : **Round off each of the following numbers to the nearest hundred, thousand, ten thousand and lakh : -

(a) 473847

(b) 534573

(c) 85364

**Solution : **

Number | Rounded to the nearest | |||
---|---|---|---|---|

Hundred | Thousand | T-Thousand | Lakh | |

473847 | 473800 | 474000 | 470000 | 500000 |

534573 | 534600 | 535000 | 530000 | 500000 |

85364 | 85400 | 85000 | 90000 | 100000 |

There are no rigid rules to estimate the outcomes on numbers. It all depends on the degree of accuracy required.

In decimal fractions, we do as follows :

Let's take some examples.

2.456

It has three decimal places.

Here, digit at third decimal places is 6 > 5.

Hence, 2.456 ≈ 2.46 (correct to two decimal places.)

again, 6 > 5,

2.46 ≈ 2.5 (correct to one decimal place)

Similarly,

32.43 ≈ 32.4 ≈ 32

32.89 ≈ 32.9 ≈ 33

20.093 ≈ 20.09 ≈ 20.1

1.0009 ≈ 1

2.99 ≈ 3

2.09 ≈ 2

Thus if decimal part has last digit ≥ 5, we add 1 to the left digit. If decimal part has last digit < 5, the second last digit remains same.