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Number - Ordering and Rounding Decimals on the Number Line

Grade 6IB

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

🔑Concepts

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Decimal Place Value: Each digit after the decimal point represents a power of 110\frac{1}{10}. For example, in 0.5730.573, 55 is in the tenths place (510\frac{5}{10}), 77 is in the hundredths place (7100\frac{7}{100}), and 33 is in the thousandths place (31000\frac{3}{1000}).

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Comparing Decimals: To compare two decimals, align the decimal points and compare digits from left to right. For example, 0.4>0.380.4 > 0.38 because 44 tenths is greater than 33 tenths.

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Decimals on a Number Line: A number line can be divided into equal intervals. Between 00 and 11, there are 1010 intervals of 0.10.1 each. Between 0.10.1 and 0.20.2, there are 1010 smaller intervals of 0.010.01 each.

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Rounding Rule: To round a decimal to a specific place (e.g., 11 decimal place), look at the digit to its right. If the digit is 5,6,7,8,5, 6, 7, 8, or 99, round up. If it is 0,1,2,3,0, 1, 2, 3, or 44, keep the digit the same.

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Equivalent Decimals: Adding zeros to the end of a decimal does not change its value. For example, 0.6=0.60=0.6000.6 = 0.60 = 0.600.

📐Formulae

Decimal Value=d1×10−1+d2×10−2+d3×10−3+…\text{Decimal Value} = d_1 \times 10^{-1} + d_2 \times 10^{-2} + d_3 \times 10^{-3} + \dots

Interval Size=Difference between markersNumber of spaces between markers\text{Interval Size} = \frac{\text{Difference between markers}}{\text{Number of spaces between markers}}

Rounding x.yz to 1 dp≈{x.yif z<5x.(y+1)if z≥5\text{Rounding } x.yz \text{ to 1 dp} \approx \begin{cases} x.y & \text{if } z < 5 \\ x.(y+1) & \text{if } z \geq 5 \end{cases}

💡Examples

Problem 1:

Arrange the following numbers in ascending order: 0.720.72, 0.0750.075, 0.70.7, and 0.7020.702.

Solution:

0.075<0.7<0.702<0.720.075 < 0.7 < 0.702 < 0.72

Explanation:

To compare, we can write them with the same number of decimal places: 0.720,0.075,0.700,0.7020.720, 0.075, 0.700, 0.702. Comparing the thousandths: 75<700<702<72075 < 700 < 702 < 720. Therefore, the order is 0.075,0.7,0.702,0.720.075, 0.7, 0.702, 0.72.

Problem 2:

Round 14.56814.568 to two decimal places.

Solution:

14.5714.57

Explanation:

We look at the third decimal place (thousandths), which is 88. Since 8≥58 \geq 5, we round up the digit in the second decimal place (hundredths) from 66 to 77.

Problem 3:

Identify the number represented by point AA on a number line if it is located exactly halfway between 3.43.4 and 3.53.5.

Solution:

3.453.45

Explanation:

The distance between 3.43.4 and 3.53.5 is 0.10.1. Half of 0.10.1 is 0.050.05. Therefore, 3.4+0.05=3.453.4 + 0.05 = 3.45.

Problem 4:

Calculate the difference between 8.58.5 and 3.273.27 using vertical subtraction.

Solution:

8.50−3.275.23\begin{array}{r} 8.50 \\ - 3.27 \\ \hline 5.23 \end{array}

Explanation:

Align the decimal points and add a placeholder zero to 8.58.5 to make it 8.508.50. Subtract 77 from 1010 (borrowing from 55), 22 from 44, and 33 from 88.

Ordering and Rounding Decimals on the Number Line Grade 6 Notes & Examples