## Tuesday, 8 November 2011

### Whole Numbers

The whole numbers are the counting numbers and 0. The whole numbers are 0, 1, 2, 3, 4, 5, ...

### Place Value

The position, or place, of a digit in a number written in standard form determines the actual value the digit represents. This table shows the place value for various positions:

 Place (underlined) Name of Position 1 000 Ones (units) position 1 000 Tens 1 000 Hundreds 1 000 Thousands 1 000 000 Ten thousands 1 000 000 Hundred Thousands 1 000 000 Millions 1 000 000 000 Ten Millions 1 000 000 000 Hundred millions 1 000 000 000 Billions
Example:
The number 721040 has a 7 in the hundred thousands place, a 2 in the ten thousands place, a one in the thousands place, a 4 in the tens place, and a 0 in both the hundreds and ones place.

### Rounding Whole Numbers

To round to the nearest ten means to find the closest number having all zeros to the right of the tens place. Note: when the digit 5, 6, 7, 8, or 9 appears in the ones place, round up; when the digit 0, 1, 2, 3, or 4 appears in the ones place, round down.
Examples:
Rounding 119 to the nearest ten gives 120.
Rounding 155 to the nearest ten gives 160.
Rounding 102 to the nearest ten gives 100.
Similarly, to round a number to any place value, we find the number with zeros in all of the places to the right of the place value being rounded to that is closest in value to the original number.
Examples:
Rounding 180 to the nearest hundred gives 200.
Rounding 150090 to the nearest hundred thousand gives 200000.
Rounding 1234 to the nearest thousand gives 1000.
Rounding is useful in making estimates of sums, differences, etc.
Example:
To estimate the sum 119360 + 500 to the nearest thousand, first round each number in the sum, resulting in a new sum of 119000 + 1000.. Then add to get the estimate of 120000.

click exercise