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Number - Whole Numbers: Place Value, Number Lines, Large Numbers, and Rounding

Grade 6IB

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

🔑Concepts

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Place Value: The value of a digit is determined by its position in a number. In the base-10 system, each position to the left is 1010 times greater than the position to its right.

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Large Numbers: Numbers are grouped into periods of three digits (units, thousands, millions, billions) separated by commas or spaces. For example, 1,000,0001,000,000 is one million and 1,000,000,0001,000,000,000 is one billion.

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Expanded Form: This represents a number as the sum of the values of its digits. For example, 4,5024,502 in expanded form is 4,000+500+0+24,000 + 500 + 0 + 2.

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Number Lines: A number line is a visual representation where numbers are placed in order from left (smaller) to right (larger). The distance between any two consecutive whole numbers is equal.

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Rounding Rules: To round to a specific place value, look at the digit to its immediate right. If that digit is 5,6,7,8,5, 6, 7, 8, or 99, round up (increase the target digit by 11). If it is 0,1,2,3,0, 1, 2, 3, or 44, round down (keep the target digit the same). All digits to the right of the target place become 00.

📐Formulae

Value=Digit×Position ValueValue = Digit \times Position\ Value

103=1,000 (One Thousand)10^3 = 1,000 \text{ (One Thousand)}

106=1,000,000 (One Million)10^6 = 1,000,000 \text{ (One Million)}

109=1,000,000,000 (One Billion)10^9 = 1,000,000,000 \text{ (One Billion)}

💡Examples

Problem 1:

Write the number 50,60450,604 in expanded form and identify the place value of the digit 66.

Solution:

Expanded form: 50,000+600+450,000 + 600 + 4. The digit 66 is in the hundreds place.

Explanation:

We break down the number based on its positions: 55 is in the ten-thousands (50,00050,000), 00 is in the thousands, 66 is in the hundreds (600600), 00 is in the tens, and 44 is in the ones (44).

Problem 2:

Compare the following numbers using >> or <<: 1,250,9001,250,900 and 1,251,0001,251,000.

Solution:

1,250,900<1,251,0001,250,900 < 1,251,000

Explanation:

Compare from the largest place value (left to right). The millions and hundred-thousands are the same. In the thousands place, 0<10 < 1, so 1,250,9001,250,900 is smaller.

Problem 3:

Round 675,492675,492 to the nearest ten-thousand.

Solution:

680,000680,000

Explanation:

The digit in the ten-thousands place is 77. The digit to its right (thousands place) is 55. Since it is 55 or greater, we round up the 77 to an 88 and change all digits to the right to 00.

Problem 4:

Perform the subtraction: 1,000,000−456,7891,000,000 - 456,789.

Solution:

1000000−456789543211\begin{array}{r} 1000000 \\ -456789 \\ \hline 543211 \end{array}

Explanation:

Align the digits by their place values and subtract, borrowing from the left where necessary.