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4. How many whole numbers are there from: \( \begin{array}{l}\text { a) }-5 \text { to } 0 \text { ? } \\ \text { 5. What are the values of these digits in the number } 1456709 \text { ? } \\ \begin{array}{ll}\text { a) } 7 & \text { b) } 4\end{array} \\ \text { 6. Write these as single numbers. } \\ \text { a) three billion, five million, four hundred and sixty-eight thousand and ten } \\ \text { b) sixty million, five hundred and four thousand and forty-two }\end{array} \) 7. Use a number line to show each number that you land on. \( \begin{array}{ll}\text { a) Start on } 2 \text {, and move } 3 \text { spaces in a negative direction. } \\ \text { b) Start on }-5 \text {, and move } 6 \text { spaces in a positive direction. } \\ \text { c) Start on }-6 \text {, and move } 5 \text { spaces in a negative direction. }\end{array} \)

Ask by Summers Lambert. in South Africa
Feb 24,2025

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4a) There are 6 whole numbers from –5 to 0. 5a) The digit 7 represents 700. 5b) The digit 4 represents 400,000. 6a) 3,005,468,010 6b) 60,504,042 7a) Starting at 2 and moving 3 spaces in a negative direction lands on –1. 7b) Starting at –5 and moving 6 spaces in a positive direction lands on 1. 7c) Starting at –6 and moving 5 spaces in a negative direction lands on –11.

Solution

Below is a step‐by‐step solution to each part of the problem: ──────────────────── 1. (Question 4a) ──────────────────── • Question: How many whole numbers are there from –5 to 0? • Interpretation: Although “whole numbers” are sometimes defined as the nonnegative integers (0, 1, 2, …), in many contexts “whole numbers” means “integers” on a number line. Since –5 is negative, here we count every integer from –5 up to 0. • List the numbers: –5, –4, –3, –2, –1, 0. • Count: There are 6 numbers. Answer for 4a: 6 ──────────────────── 2. (Question 5) ──────────────────── • Question: What are the values of these digits in the number 1,456,709? – a) the digit 7 – b) the digit 4 Step 1. Write the number with its place values:   1  4  5  6  7  0  9   |  |  |  |  |  |  |   M HTh TTh Th H  T  O   (million, hundred‑thousands, ten‑thousands, thousands, hundreds, tens, ones) a) For the digit 7:  – Its position is the hundreds place.  – Value: 7 × 100 = 700. b) For the digit 4:  – Its position is the hundred‑thousands place.  – Value: 4 × 100,000 = 400,000. Answer for 5a: 700 Answer for 5b: 400,000 ──────────────────── 3. (Question 6) ──────────────────── • Write these names as single numbers. a) “three billion, five million, four hundred and sixty‑eight thousand and ten”  – Break it down:   • Three billion = 3,000,000,000   • Five million = 5,000,000   • Four hundred and sixty‑eight thousand = 468,000   • And ten = 10  – Add them together:   3,000,000,000 + 5,000,000 = 3,005,000,000   3,005,000,000 + 468,000 = 3,005,468,000   3,005,468,000 + 10 = 3,005,468,010 Answer for 6a: 3,005,468,010 b) “sixty million, five hundred and four thousand and forty‑two”  – Break it down:   • Sixty million = 60,000,000   • Five hundred and four thousand = 504,000   • And forty‑two = 42  – Add them together:   60,000,000 + 504,000 = 60,504,000   60,504,000 + 42 = 60,504,042 Answer for 6b: 60,504,042 ──────────────────── 4. (Question 7) ──────────────────── • Use a number line to show each number you land on after starting at the given point and moving the specified number of spaces. a) Start on 2, and move 3 spaces in a negative direction.  • Calculation: 2 – 3 = –1  • On the number line, you start at 2 and then step left three units to land at –1.   b) Start on –5, and move 6 spaces in a positive direction.  • Calculation: –5 + 6 = 1  • On the number line, you start at –5 and then step right six units to land at 1.   c) Start on –6, and move 5 spaces in a negative direction.  • Calculation: –6 – 5 = –11  • On the number line, start at –6 and then step left five units to end at –11. ──────────────────── Summary of Answers: ──────────────────── 4a) 6 whole numbers. 5a) The digit 7 represents 700. 5b) The digit 4 represents 400,000. 6a) 3,005,468,010 6b) 60,504,042 7a) You land on –1. 7b) You land on 1. 7c) You land on –11. These complete the solutions to the given problems.

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Extra Insights

Did you know that number line activities date back to ancient civilizations? The Babylonians used similar concepts around 2000 BC to represent numbers and perform calculations. They often utilized a base-60 system, which might seem a bit quirky today, but it laid the foundation for how we unravel numerical relationships! Visualizing numbers on a number line is not just academic; it’s a real-world application that helps us understand distances, time, and even financial data. For instance, budgeting can be thought of as a number line where you track income and expenses. This method not only clarifies where you stand but also helps you plan for the future like a financial pro while avoiding pitfalls along the way!

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