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Fractions and Decimals - Relating Fractions to Decimals

Grade 4IB

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Understanding Tenths: A tenth is one of ten equal parts of a whole. In fraction form, it is written as 110\frac{1}{10}. In decimal form, it is written as 0.10.1. Visually, imagine a long chocolate bar divided into 1010 equal vertical segments; shading one segment represents 0.10.1.

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Understanding Hundredths: A hundredth is one of one hundred equal parts of a whole. It is written as 1100\frac{1}{100} or 0.010.01. Visually, think of a large square grid consisting of 100100 tiny squares (1010 rows and 1010 columns); shading just one tiny square represents 0.010.01.

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The Decimal Point: The decimal point is a period used to separate the whole number part from the fractional part. In the number 12.3412.34, the digits to the left (1212) are whole numbers, and the digits to the right (3434) represent parts of a whole. Visually, the decimal point acts as a 'fence' between the ones place and the tenths place.

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Place Value Chart: Decimals follow a specific place value system. To the right of the decimal point, the first position is the Tenths place (value of 110\frac{1}{10}) and the second position is the Hundredths place (value of 1100\frac{1}{100}). You can visualize this on a table where the columns are labeled: Tens, Ones, [Decimal Point], Tenths, Hundredths.

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Relationship between Tenths and Hundredths: Ten hundredths are equivalent to one tenth (1010 hundredths =1= 1 tenth). This means 10100=110\frac{10}{100} = \frac{1}{10} or 0.10=0.10.10 = 0.1. Visually, filling 1010 small squares in a hundred-grid covers exactly one full column, which is the same as one-tenth of the total grid.

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Converting Fractions to Decimals: To convert a fraction with a denominator of 1010 or 100100 to a decimal, look at the number of zeros. A denominator of 1010 means there is 11 digit after the decimal point (e.g., 610=0.6\frac{6}{10} = 0.6). A denominator of 100100 means there are 22 digits after the decimal point (e.g., 6100=0.06\frac{6}{100} = 0.06).

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Mixed Numbers as Decimals: A mixed number like 25102 \frac{5}{10} combines a whole number and a fraction. It is written as 2.52.5. Visually, this represents two fully shaded shapes and one shape with only 55 out of 1010 parts shaded.

📐Formulae

n10=0.n\frac{n}{10} = 0.n

n100=0.0n\frac{n}{100} = 0.0n (where nn is a single digit)

nn100=0.nn\frac{nn}{100} = 0.nn (where nnnn is a two-digit number)

Whole NumberNumeratorDenominator=Whole Number.Decimal Part\text{Whole Number} \frac{\text{Numerator}}{\text{Denominator}} = \text{Whole Number}.\text{Decimal Part}

1 Tenth=10 Hundredths1 \text{ Tenth} = 10 \text{ Hundredths}

💡Examples

Problem 1:

Convert the following fractions into decimal form: a) 710\frac{7}{10} and b) 42100\frac{42}{100}.

Solution:

Step 1: For 710\frac{7}{10}, since the denominator is 1010, there is one decimal place. Place the 77 in the tenths column to get 0.70.7. \ Step 2: For 42100\frac{42}{100}, since the denominator is 100100, there are two decimal places. Place the 44 in the tenths place and the 22 in the hundredths place to get 0.420.42.

Explanation:

We use the denominator to determine the place value position. Tenths (1010) require one digit after the decimal, and hundredths (100100) require two.

Problem 2:

Write the mixed number 531005 \frac{3}{100} as a decimal and identify the digit in the hundredths place.

Solution:

Step 1: Identify the whole number, which is 55. Write it before the decimal point: 5.5.. \ Step 2: Convert the fraction 3100\frac{3}{100} to a decimal. Since it is hundredths, there must be two places. The 33 goes in the second place, and we use 00 as a placeholder for the tenths: 0303. \ Step 3: Combine them: 5.035.03. \ Step 4: Identify the hundredths place, which is the second digit after the decimal: 33.

Explanation:

To write hundredths for single-digit numerators, a zero must be used in the tenths place as a placeholder.