Year 7 Maths: Decimal Number

What Decimal Number is Illustrated?

Decimals are numbers that show parts of a whole. Decimals use a decimal point (.) to separate whole numbers from fractions of whole numbers. We can think of decimals as breaking down numbers into tenths, hundredths, and thousandths, depending on how many parts we divide the number into.

Example: Illustrating Decimals with a Picture

Imagine a grid of 100 squares. Some of these squares are shaded. Each square represents one hundredth of the whole. If 6 squares are coloured, it shows six hundredths of the grid.

Here’s how we write that as a decimal:

So, six hundredths can be written as 0.06.

Understanding Decimal Place Values:

• The first place after the decimal point is called the tenths place. It shows parts of the number divided into ten.
• The second place is the hundredths place. It shows parts of the number divided into one hundred.
• The third place is the thousandths place, for numbers divided into one thousand.

For example:

• 0.3 means three tenths.
• 0.25 means two tenths and five hundredths.
• 0.678 means six tenths, seven hundredths, and eight thousandths.

Key Rules:

1. Decimal point separates whole numbers from fractions of whole numbers.
2. The place value of each digit depends on how far it is from the decimal point.

• 0.5 is “five tenths”.
• 0.07 is “seven hundredths”.

1. Tenths come first, then hundredths, and then thousandths.

Tips & Tricks:

• Tenths: If you divide 1 whole into 10 equal parts, each part is a tenth.
• Hundredths: If you divide 1 whole into 100 equal parts, each part is a hundredth.
• Visualizing: Grids or pie charts are helpful for understanding decimals.

Questions on “What Decimal Number is Illustrated?”

Easy Difficulty:

1. A grid of 10 squares shows 3 shaded. What decimal is this?
2. What decimal is represented by 5 shaded squares out of 100?
3. How do you write seven tenths as a decimal?
4. A grid has 2 shaded squares out of 100. What is this as a decimal?
5. If 1 square is shaded out of 10, what decimal is shown?
6. What decimal represents 9 shaded squares out of 100?
7. Write four tenths as a decimal.
8. If 6 squares are shaded out of 10, what decimal is shown?
9. What decimal is represented by 4 squares shaded out of 100?
10. Write five hundredths as a decimal.
11. If 8 squares are shaded out of 100, what decimal is represented?
12. Write two tenths as a decimal.
13. A grid has 7 shaded squares out of 100. What is this as a decimal?
14. If 0.3 is shown, how many tenths are coloured?
15. What decimal is represented by 10 shaded squares out of 100?
16. Write 1 tenth as a decimal.
17. A grid has 5 shaded squares out of 100. What decimal is represented?
18. Write nine tenths as a decimal.
19. What decimal represents 3 shaded squares out of 10?
20. A grid shows 6 shaded squares out of 100. What is the decimal?

Medium Difficulty:

1. A grid of 100 squares has 15 shaded. What decimal is represented?
2. Write twelve hundredths as a decimal.
3. A grid shows 36 shaded squares out of 100. What decimal is shown?
4. If 8 tenths are shaded, what decimal is represented?
5. Write 0.07 as a fraction out of 100.
6. What decimal represents 19 shaded squares out of 100?
7. A grid shows 25 shaded squares out of 100. What is the decimal?
8. Write fifty-four hundredths as a decimal.
9. If 0.4 is represented, how many tenths are shaded?
10. A grid of 10 squares has 9 shaded. What decimal is represented?
11. What decimal represents 23 shaded squares out of 100?
12. Write eight hundredths as a decimal.
13. A grid shows 7 tenths shaded. What decimal is shown?
14. Write seventy-five hundredths as a decimal.
15. A grid of 100 squares has 88 shaded. What decimal is represented?
16. What decimal is represented by 13 shaded squares out of 100?
17. Write 0.08 as a fraction out of 100.
18. A grid shows 55 shaded squares out of 100. What decimal is shown?
19. Write twenty-one hundredths as a decimal.
20. If 0.9 is represented, how many tenths are shaded?

High Difficulty:

1. A grid of 100 squares shows 67 shaded. What decimal is represented?
2. Write forty-two hundredths as a decimal.
3. A grid of 100 squares has 91 shaded. What decimal is shown?
4. If 99 hundredths are shaded, what decimal is represented?
5. Write 0.08 as a fraction out of 100.
6. A grid shows 83 shaded squares out of 100. What decimal is represented?
7. Write sixty-eight hundredths as a decimal.
8. A grid shows 27 hundredths shaded. What decimal is represented?
9. What decimal represents 92 shaded squares out of 100?
10. Write 0.14 as a fraction out of 100.
11. A grid of 100 squares has 73 shaded. What decimal is shown?
12. Write fifty-five hundredths as a decimal.
13. A grid of 100 squares has 99 shaded. What decimal is shown?
14. Write 0.33 as a fraction out of 100.
15. A grid shows 87 hundredths shaded. What decimal is shown?
16. Write seventy-three hundredths as a decimal.
17. A grid shows 42 shaded squares out of 100. What decimal is represented?
18. Write 0.89 as a fraction out of 100.
19. A grid of 100 squares has 94 shaded. What decimal is represented?
20. Write 0.76 as a fraction out of 100.

These questions will help you practice converting between visuals and decimals and get more comfortable with place values like tenths and hundredths. Keep working through examples, and you’ll soon master this skill!