In mathematics, usually in third to fifth grade, students are introduced to different types of numbers and problems based on those. They learn about decimal numbers too. Initially students are quite confused about decimals. But decimal numbers are very easy to work with. Tutorvista provides a very helpful tutorial about decimal numbers. A decimal number is a point representation of numbers. A number which has a fractional part in it, known as a decimal number. It has some numbers after a decimal point too. For example - 3.5 , 0.0006, 412.93, 5984.01 etc.
Equivalent decimal numbers are the numbers which indicate the same fraction of the whole. Based on the number of decimal digits in a decimal number: 34.0 and 34.00 are two equivalent decimals. Also, 1.5 and 1.50 are also two equivalent decimal numbers. Every fraction term is simply written as decimals. For example, $\frac{4}{5}$ fraction should be written in decimal as 0.8.
The decimal number 0.5 denotes a fraction $\frac{5}{10}$ and 0.5 also represents the fraction $\frac{50}{100}$. While, the decimal number 0.25 denotes the fraction $\frac{25}{100}$. But eventually, it also represents the fraction $\frac{2500}{1000}$. Decimal fractions always
have a denominator based on a power of 10.
A decimal fractions may be changed into equivalent fractions of higher or lower terms,as only if the case with common fractions. If each decimal fraction is rewritten in its common fraction form, we change the higher terms that is accomplished by multiplying both numerator and denominator by 10 or 100 (Some higher power of 10).
An equivalent decimals is something which is equal to the decimal and the fractions that you can see below with an examples.
For example, $\frac{3}{4}$ is equal to the 0.75, This seems decimals is equal to the fractions.
An equivalent decimal must has the same digits after the decimal point.
A number of zero’s added at the end of the decimal digits in decimal number should not change the value of given decimal.
A number of zero’s added before the whole number part of the decimal number should not change the value of decimal.
For equivalent decimals, the place values cannot be changed.
Example:
Consider a decimal 8.250. An equivalent decimal of this decimal is 000008.25000000 If we check the place values of 8, 2 and 5, it cannot be changed.
Equivalent fraction values for decimal numbers:
Chart with respect to millimeter:
The above chart explains how decimal numbers are converted to millimeters and how a fraction is converted into decimal number. Decimal can be converted into millimeter by multiplying it with 25.4 as 1 inch = 25.4 millimeters.
Decimal chart:
Fractions | Decimals | Powers of ten |
1/10(tenths) 1/100(hundredths) 1/1000(thousandths) 1/10,000(ten thousandths) 1/100,000(hundred thousandths) | 0.1 0.01 0.001 0.0001 0.00001 | 10^{-1} 10^{-2} 10^{-3} 10^{-4} 10^{-5} |
It represents the decimal equivalent of a fraction and decimal values in powers of ten.
Chart with its square root and squares:
Fraction | Decimal | Square | Square root |
1/17 2/25 3/37 12/32 11/16 | 0.058 0.08 0.081 0.375 0.687 | 0.0034 0.0064 0.0065 0.1406 0.4726 | 0.242 0.282 0.284 0.612 0.829 |
Chart is presented with the square and square root of its decimal numbers with its corresponding fraction number.
Solved Examples
Question 1: Which of the following decimal is equivalent to 0.36?
a) 36
b) 3.6
c) 00.3600
d) 1.36
Solution:
Given decimal is 0.36.
The place value of 0.36 is 3 is in tenth place ($\frac{1}{10}$) and 6 is in hundredth place ($\frac{1}{100}$).
Now check the place value of given options which are equal to place values of 0.36 decimal.
Option a: 36
The place value of 6 is ones and 3 is tens which is not equivalent to 0.36.
Option b: 3.6
The place value of 6 is tenths ($\frac{1}{10}$) and 3 is ones which is not equivalent to 0.36.
Option c: 00.3600
The place value of 3 is tenths and 3 is hundredths which is equivalent to 0.36.
Correct answer is (c) 00.3600
Question 2: Which of the following decimal is equivalent to 23.6?
a) 2.36
b) 0000023.60000
c) 0.236
d) 20.36
Solution:
Given decimal is 23.6.
The place value of 23.6 is,
In 23, 3 is in ones place and 2 is in tens place. In decimal point 0.6, 6 is in tenths place ($\frac{1}{10}$).
Option a: 2.36
The place value of 2 is ones and 3 is in tenths and 6 is in hundredths which is not equivalent to 0.36.
Option b: 0000023.60000
3 is in ones place, 2 is in tens place and 6 is in tenths place ($\frac{1}{10}$) which is equivalent to 23.6
Correct answer is (b) 0000023.60000 Practice Problems
Question 1: Which of the following decimal is equivalent to 55.63?
a) 5536
b) 00.55
c) 0055.6
d) 5.563
Question 2: Which of the following decimal is equivalent to 0.0063?
a) 00.00063
b) 0.63
c) 00.006300
d) 0.630