Counting in groups

Counting objects not exceeding one billion (1 000 000 000) in groups of ten million

Counting ten million shillings (10 000 000) formed by a bundle of one thousand banknotes of ten thousand shillings.

When you count ten bundles of ten million shillings each (or when you count 10 000 banknotes of ten thousand shillings), you will form a bundle with a total of one hundred million (100 000 000).

In numerals, one hundred million is written as 100 000 000, and in words it is written as one hundred million. The number 10 000 000 is formed using eight digits, whereas 100 000 000 is formed using nine digits.

When you count ten bundles of one hundred million shillings each (or when you count 100 000 banknotes of ten thousand shillings), you will form bundles with a total of one billion shillings. In numerals, this number is written as 1 000 000 000 and in words, it is written as one billion. The number 100 000 000 is formed using nine digits, but 1 000 000 000 is formed using ten digits.

The following activities will help you to understand how to count objects in groups up to one billion easily:

Place values and total values of digits in numbers not exceeding 1 000 000 000

One billion or 1 000 000 000 in numerals has ten digits. Also, any whole number between ten million and one billion is formed using eight or nine digits. In this section, you will learn how to identify place values of digits in numbers that do not exceed one billion. You will also learn how to identify the total values of digits of such numbers.

The place value and total value of a digit in a number depend on the position of the digit in the given number. The total value of a digit increases from the right to the left corresponding to the place value of the digit in the number.

First, identify ones, followed by tens, hundreds, thousands, ten thousands, and so on depending on the number of digits in the given number.

Example 1

Arrange the digits of 1 000 000 000 in their corresponding place values.

Answer

The number 1 000 000 000 has ten digits. Thus, it has ten positions of place values. The place value of each digit in 1 000 000 000 is as follows:

You can also arrange the digits in their place values as follows:

1 is in billions

0 is in hundred millions

0 is in ten millions

0 is in millions

0 is in hundred thousands

0 is in ten thousands

0 is in thousands

0 is in hundreds

0 is in tens, and

0 is in ones.

Example 2

Write 912 834 567 by showing:

(a) The place value of each digit

(b) The total value of each digit.

Answer

Example 3

Write the place value of 6 and the total value of 4 in 678 945 231.

Solution

The following table shows the place value of each of the digits in 678 945 231.

Therefore, the place value of 6 in 678 945 231 is hundred millions.

The total value of 4 in 678 945 231 is 40 000.

Example 4

Write the following numbers in their expanded form:

(a) 789 273 453

(b) 132 261 514

Solution

Recall that, to write a number in its expanded form is to write it using the total values of each of its digits. Each total value is joined using addition operation.

(a) 789 273 453 = 700 000 000 + 80 000 000 + 9 000 000 + 200 000 + 70 000 + 3 000 + 400 + 50 + 3

(b) 132 261 514 = 100 000 000 + 30 000 000 + 2 000 000 + 200 000 + 60 000 + 1 000 + 500 + 10 + 4