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Let’s begin with a quick question. Which of the following are digits?
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A digit is any integer from 0 to 9.
0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are the ten digits.
Digits are used to make numbers.
In the earlier question:
- 21 is a two-digit number made up of the digits “2” and “1”.
- 145.9 is a 4-digit number made up of the digits “1”, “4”, “5”, and “9”.
- 200 is a 3-digit number made up of the digits “2” and “0”.
- -9 is a 1-digit number made up the digit “9”.
- and finally, -100 is a 3-digit number made up of the digits “1” and “0”.
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Is 00025.107900 an 11-digit number?
Solution: You probably know that you can attach zeros to the beginning of a number without changing its value. So, 00025.107900 and 25.107900 are basically the same. Similarly, the value of a number does not change if you attach a sequence of zeros to the right of a decimal point after which no non-zero digit follows. So, 25.107900 and 25.1079 are also the same. Make sure that you don’t attach or remove the other zero ( 25.1079). Removing this 0 will change the value as 25.1079 and 25.179 are not the same values. When counting the digits of a number, we discard those 0’s that do not change the value of the number. Hence 00025.107900 is not an 11-digit number since 00025.107900 is the same as 25.1079. Therefore, it is a 6-digit number. |
Some questions refer to the “units digit” (also known as the “ones” digit), the “tens digit”, or even the “tenths digit” of a number. Units, tens, and tenths are all titles indicating the position of every digit in that number.
Let’s discuss these titles with an example.
Suppose we have a number, 42936.875
- The “units”(ones) digit is the digit directly to the left of the decimal point. In this case, it is 6.
- The “tens” digit is the digit in the second place to the left of the decimal point. The tens digit of 42936.875 is “3”.
- The “tenths” digit is the digit directly to the right of the decimal point. The tenths digit of 42936.875 is “8”.
Note that unlike the left side of the decimal point, which begins with a “units digit”, the right side begins directly with a “tenths digit”.
What is the position of the digit “4” in 42936.875?
Note that the positions to the right of the decimal point end in “ths“. Questions usually does not go beyond 3 to 4 positions on either side of the decimal point. So, knowing the titles up to the thousands and thousandths position is perfectly ok. |
You can memorize the following table to remember the position of each digit in a number to the left of the decimal point.
| ten millions | millions | hundred thousands | ten thousands | thousands | hundreds | tens | units/ones | . |
and the following table to remember the position of each digit in a number to the right of the decimal point.
| . | tenths | hundredths | thousandths | ten thousandths | hundred thousandths | millionths | ten millionths |
Now that you know about the titles of the various positions in a number, let’s talk about place value.
Every digit in a number has a place value.
Place Value is defined as the product of a digit and its position within that number.
For example, in 42936.875,
- the digit “6” is in the units/ones position and its place value is 6 = 6 × 1
- the digit “3” is in the tens position and its place value is 30 = 3 × 10
- the digit “9” is in the hundreds position and its place value is 900 = 9 × 100
- the digit “2” is in the thousands position and its place value is 2,000 = 2 × 1000
- the digit “4” is in the ten thousands position and its place value is 40,000 = 4 × 10,000
- the digit “8” is in the tenths position and its place value is 0.8 = 8 × 1/10
- the digit “7” is in the hundredths position and its place value is 0.07 = 7 × 1/100
- the digit “5” is in the thousandths position and its place value is 0.005 = 5 × 1/1000
Understanding the place value of digits helps in writing numbers in their expanded form.
The expanded form is simply the sum of the place values.
For example: the expanded form of 42936.875 is:
= 4 × 10,000 + 2 × 1000 + 9 × 100 + 3 × 10 + 6 × 1 + 8 × 1/10 + 7 × 1/100 + 5 × 1/1000
= 40,000 + 2000 + 900 + 30 + 6 +0.8 + 0.07 + 0.005
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xy represents a positive two-digit integer, where x and y are digits. Which of the following is the expanded form of xy?
In xy, x is at the tens position and y is at the units/ones position. Therefore the place value of x is 10 * x and the place value of y is y * 1 Expanded form is simply the sum of the place values. Hence the expanded form becomes 10x + y. |
xy represents a positive two-digit integer, where x and y are digits. Which of the following cannot be the value of the sum of x and y?
Since xy is a positive two-digit integer, it could have any value from 10 to 99, inclusive. 10, 11, 12, 13 …. , 99 The question focuses on the sum of the digits. i.e. x + y For example, 65 is a two-digit integer, and the sum of its digits is 6 + 5 = 11. Let’s evaluate all the options, one by one.
So if we have a 2-digit integer like 99, the maximum possible sum is 18. |