Model and express a fraction, including mixed numbers and fractions greater than one, with the denominator 10 as an equivalent fraction with the denominator 100.

Use decimal notation to represent fractions with denominators of 10 or 100, including mixed numbers and fractions greater than 1, and use fractional notation with denominators of 10 or 100 to represent decimals.

Explore the addition of a fraction with denominator of 10 to a fraction with denominator of 100 using equivalent fractions.

Identify the number that is one-tenth more, one-tenth less, one-hundredth more and one-hundredth less than a given number.

Explore the addition and subtraction of multi-digit numbers with decimals to the hundredths.

Decimals and fractions are both ways of representing parts of a whole. In fourth grade, students learn that decimals can be expressed as fractions with a denominator of 10 or 100 (or any multiple of 10).

The following examples show familiar fraction models to demonstrate different decimal amounts.

The place value chart, which students have learned in previous grade levels, now includes decimal parts. In fourth grade, students work with numbers through the hundredths place.

Understanding the connection between the fractional part and the decimal equivalent helps students to conceptualize decimals. In this example, the fractional part "eight tenths" is represented as both a fraction, 8/10, and as a decimal, .8. When students begin working with decimals, they will need to practice recording numbers in the place value chart so that they can remember the names and meanings of the tenths and hundredths place values.

This example shows twenty-three hundredths in fraction and decimal form. At first, students may struggle to understand that .8 is larger than .23. Seeing the two numbers represented on a fraction diagram like the one shown below is essential to helping students understand this concept.

Students may have been taught that when you multiply a number by 10, you add a zero to the end. Even though this is a useful trick in third grade, it is mathematically inaccurate, and can lead to confusion when working with decimals in later grades. The diagram below shows that adding a zero to the end of a decimal does not change the meaning of the number, since it multiplies both the numerator and denominator of the fractional part by 10, and multiplying by 10/10 is the same as multiplying by 1 whole, which results in the same number. In later grades, students will be introduced to the idea of "moving the decimal point." For now, students simply need to understand that adding a zero to the end of a decimal does not change the number's value.

Adding tenths and hundredths can give students trouble if they do not have a solid conceptual understanding of how tenths and hundredths relate. Seeing a visual model, and understanding that .2 = .20 can help students to add these fractional parts correctly.

This decimal representation also illustrates that .2 = .20, so .20 + .46 = .66.