Understanding Tenths and Hundredths in Decimals and Fractions
Decimals and fractions are two ways to represent parts of a whole, especially when dealing with tenths and hundredths. These concepts come up often in Key Stage 3 maths, so let’s explore what they mean, how to work with them, and how they can be visualized using models.
What Are Tenths?
When something is divided into ten equal parts, each part is called a “tenth.” For example, if you take a square and split it into ten equal pieces, each piece is one-tenth of the whole. If three of those pieces are shaded, you have three-tenths of the square shaded. We can write three-tenths as a fraction, 3⁄10, or as a decimal, 0.3. Both forms represent the same amount—they’re just different ways of writing it!
In one example, we might compare 0.6 and 7⁄10. To make this easier, we can convert each number to tenths: 0.6 is the same as 6⁄10, so it’s a bit smaller than 7⁄10. Understanding that each tenth is like adding 0.1 helps when comparing values in tenths.
Another example could be “How many tenths are in 1.3?” Here, we have 1 whole and 3 tenths, which gives us 13 tenths in total. Thinking in terms of tenths shows us that decimals and fractions are closely related: 1.3 equals 13⁄10.
Working with Hundredths
Moving from tenths to hundredths simply means dividing each tenth into ten more pieces. Now, instead of 10 pieces in the whole, we have 100. Each part is a hundredth of the whole. For instance, if we shade 45 parts out of 100, that’s 45 hundredths, or 0.45 as a decimal. Similarly, we could write it as 45⁄100.
Hundredths allow us to see more detail in decimals. For example, 0.07 is 7 hundredths, and we can write it as 7⁄100. But be careful with place value! A common mistake is to write 0.07 as 7⁄10, which is actually 0.7. Notice the difference: 7 hundredths is much smaller than 7 tenths.
Another important concept is expressing whole numbers in terms of hundredths. For example, 100 can be thought of as 10,000 hundredths because 100 times 100 equals 10,000. Similarly, 56 can be written as 5600 hundredths, since 56 × 100 = 5600. Breaking down whole numbers into hundredths or tenths helps us better understand the relationship between decimals and fractions.
How Decimal Models Help
Visual models, like squares divided into parts, are very helpful for understanding tenths and hundredths. In these models, each square represents one whole. When a square is divided into 10 parts, each part represents a tenth. When it’s divided into 100 parts, each part represents a hundredth.
For instance, if a model shows 7 out of 10 parts shaded, that’s seven-tenths or 0.7. If it shows one whole square shaded and 9 extra tenths shaded in another square, that represents 1.9 or 19⁄10.
If we’re working with hundredths, each part of the square represents one-hundredth. By counting the shaded parts, we can see values like 0.78, which is 78 out of 100 parts shaded, or 78 hundredths. Grouping and counting helps avoid common mistakes, like misplacing digits. For example, it’s easy to mistakenly write 9 hundredths (0.09) as 9 tenths (0.9), but counting carefully ensures accuracy.
Combining Whole Numbers and Decimals
Sometimes, we work with a combination of whole numbers and fractions or decimals. For example, 2.82 is the same as 2 whole squares and 82 out of 100 parts shaded in the third square, which is two and eighty-two hundredths. Similarly, in models, if we see a whole square plus a few tenths shaded in the next square, we can write it as a decimal, like 1.6, or a fraction, like 16⁄10.
