What are equivalent decimals with definition and solved examples
Decimals are a way of representing fractions. Decimals can be divided into two types. The first is terminating decimals and the second one is non-terminating decimals. Terminating decimals are those which get terminated after some digits of decimal (.). For example, 2.34. Here, after 2 digits of a decimal, the number gets terminated hence, it’s a terminating decimal. Non-terminating decimals are those decimals that do not get terminated. For example 2.33333..., here 3 is repeating after the decimal. Equivalent decimals 4th grade, equivalent decimals games, equivalent decimals worksheets grade 5 are easily available on various ed-tech platforms online.
What is the Decimal Equivalent?
When two decimals are representing the same fraction, they are called the decimal equivalent. In other words, equivalent decimals are decimals that are equal. Hence they are also called equal decimals.
Let us take an example: consider the decimals 0.5 and 0.50. Here the first decimal number reflects half of something if we convert the first decimal into a fraction we get. It means if we do 10 equal partitions of something out of which we are considering only 5. On the other hand, if we convert the second decimal which is 0.50 into a fraction we get \[\frac{59}{100}\]. It means if we do 100 equal partitions of something out of which we are considering only 50. We can also simplify both of the fraction and both will end up as \[\frac{1}{2}\]. Since both the decimals are representing the same fraction, they are decimal equivalent.
[Image will be Uploaded Soon]
Like and Unlike Decimals
Decimals can also be classified as like and unlike decimals. Like decimals are decimals that have the same number of decimal places after the decimal point. For example, 2.35 and 4.67 are like decimals because they both have the same number of decimal places and that is 2.
On the other hand, decimals are decimals that don’t have the same number of decimal places after the decimal point. For example, 2.35 and 4.7 are unlike decimals because they don’t have the same number of decimal places after the decimal point. 2.35 have 2 decimal places whereas 4.7 have only one. Students may find like and unlike decimals worksheets on the Internet. The worksheet helps students to practice questions of like and unlike decimals worksheets.
Did You Know?
When we place zero after the rightmost digit in the decimal number, the value of the number remains the same. Such zeros are known as trailing zeros and they don’t affect the number.
For example, 0.1 is the same as 0.10. And 0.10 is the same as 0.100. All these numbers are decimal equivalent to each other. This is because decimal numbers are equivalent to fractions.
Keep in mind that zeros before the last digit of decimal will change the number and it’ll affect the number a lot. Such numbers can’t be decimal equivalent. For example, consider the number 0.3. Now let’s place a zero before 3. That makes the number ais 0.03.
[Image will be Uploaded Soon]
They don’t acquire the same amount of space in the grid hence they are not equivalent.
At the end of the 4th century BC, the Chinese first developed the decimal fraction concept. From there it spread to the Middle East and then to Europe.
FAQs on Understanding Equivalent Decimals in Maths
1. What are equivalent decimals?
Equivalent decimals are decimal numbers that represent the same value even though they look different. They may have different numbers of digits after the decimal point but still equal the same quantity.
- Example: 0.5, 0.50, and 0.500 are equivalent decimals.
- Adding zeros to the right of a decimal does not change its value.
- They represent the same point on a number line.
2. How do you find equivalent decimals?
You find equivalent decimals by adding or removing zeros to the right of the decimal number without changing its value. Follow these steps:
- Write the original decimal number.
- Add one or more zeros to the right of the last digit.
- Check that the place value remains the same.
3. Why does adding zeros not change the value of a decimal?
Adding zeros to the right of a decimal does not change its value because zeros in smaller place values represent nothing extra. For example:
- In 0.40, the 4 is in the tenths place and the 0 is in the hundredths place.
- The zero adds no additional value.
- So, 0.4 = 0.40.
4. Are 0.5 and 0.50 equivalent decimals?
Yes, 0.5 and 0.50 are equivalent decimals because they represent the same numerical value. In both numbers:
- 5 is in the tenths place.
- The extra zero in 0.50 is in the hundredths place.
- The value remains five-tenths.
5. How are equivalent decimals related to equivalent fractions?
Equivalent decimals and equivalent fractions represent the same value written in different forms. For example:
- 0.5 = 1/2
- 0.25 = 1/4
- 0.75 = 3/4
6. Can you give an example of equivalent decimals?
An example of equivalent decimals is 0.35, 0.350, and 0.3500. These decimals are equal because:
- They all represent thirty-five hundredths.
- Extra zeros appear in smaller place values.
- The overall value does not change.
7. What is the difference between equivalent decimals and equal decimals?
There is no difference between equivalent decimals and equal decimals; both mean decimals that have the same value. The term “equivalent” emphasizes that the numbers may look different.
- Example: 0.6 = 0.60
- They are written differently but represent the same amount.
8. How do you check if two decimals are equivalent?
You check if two decimals are equivalent by aligning place values and comparing digits. Steps:
- Add zeros to make the decimals the same length.
- Compare each digit from left to right.
- If all digits match, they are equivalent.
9. Do equivalent decimals represent the same point on a number line?
Yes, equivalent decimals represent the same point on a number line. Even if written differently:
- 0.9 and 0.90 are plotted at the same location.
- Their distance from zero is identical.
10. What are common mistakes when working with equivalent decimals?
A common mistake with equivalent decimals is thinking that more digits mean a larger value. Key points to remember:
- Adding zeros to the right does not increase value.
- Removing non-zero digits changes the value.
- Always compare place values carefully.
