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Chapter 1
Number Systems and Place Value
Key Concepts
Whole numbers, fractions, and decimals help us count, measure, and compare things. You need these skills to solve problems with money, lengths, food, and scores.
• Place value tells the value of a digit. In 4,582, the 5 means 500. - Compare whole numbers from the left. The first different digit decides. - To order numbers, arrange them from smallest to largest or largest to smallest. - Fractions show equal parts. In 3/4, 3 is the numerator and 4 is the denominator. - Equivalent fractions have the same value, such as 1/2 = 2/4. - Add or subtract fractions with the same denominator by working with the numerators. - Decimals use place values: tenths, hundredths, and thousandths. - Add zeros to compare decimals: 0.6 = 0.60.
Before you continue: Can you explain why 0.7 is greater than 0.65?
Key Terms
Place value - The value of a digit because of its position.
Numerator - The top number in a fraction.
Denominator - The bottom number in a fraction.
Equivalent fractions - Fractions with the same value.
Decimal - A number with a decimal point.
Ascending order - Arranging numbers from smallest to largest.
Descending order - Arranging numbers from largest to smallest.
Active Recall
Place value ________________________________________________ ________________________________________________
Numerator ________________________________________________ ________________________________________________
Denominator ________________________________________________ ________________________________________________
Equivalent fractions ________________________________________________ ________________________________________________
Decimal ________________________________________________ ________________________________________________
Worked Examples
1. Compare whole numbers
Compare 4,305 and 4,350.
1. Thousands are equal: 4 = 4. 2. Hundreds are equal: 3 = 3. 3. Tens differ: 0 is less than 5. 4. Therefore, 4,305 < 4,350.
Now you try: Compare 7,208 and 7,280. ________________________________________________ ______________________________________________ ________________________________________________
2. Add fractions
Find 2/7 + 3/7.
1. The denominators are the same. 2. Add the numerators: 2 + 3 = 5. 3. Keep the denominator: 2/7 + 3/7 = 5/7.
Now you try: Find 1/9 + 4/9. ________________________________________________ ______________________________________________ ________________________________________________
3. Order decimals
Arrange 0.8, 0.35, and 0.56 from smallest to largest.
1. Write equal places: 0.80, 0.35, 0.56. 2. Compare the tenths: 3, 5, and 8. 3. Order: 0.35, 0.56, 0.80.
Now you try: Order 0.4, 0.09, and 0.27. ________________________________________________ ______________________________________________ ________________________________________________
Practice Questions
1. (Easy) What is the place value of 6 in 6,214? ________________________________________________ ______________________________________________ ________________________________________________
2. (Easy) Circle the greater number: 3,901 or 3,109. ________________________________________________ ______________________________________________ ________________________________________________
3. (Medium) Arrange 45, 54, 405, and 504 in ascending order. ________________________________________________ ______________________________________________ ________________________________________________
4. (Medium) Find 3/8 + 2/8. ________________________________________________ ______________________________________________ ________________________________________________
5. (Medium) Find 7/10 - 3/10. ________________________________________________ ______________________________________________ ________________________________________________
6. (Hard) Arrange 0.7, 0.07, 0.77, and 0.17 from largest to smallest. ________________________________________________ ______________________________________________ ________________________________________________
Answer Key
1. Thousands 2. 3,901 3. 45, 54, 405, 504 4. 5/8 5. 4/10 or 2/5 6. 0.77, 0.70, 0.17, 0.07
Exam Tips & Common Mistakes
• Do not compare only the last digit. Compare digits from the left. - Do not add fraction denominators when they are equal. Keep the denominator. - Do not forget decimal zeros. Write 0.5 as 0.50 when comparing. - Check the order words. “Ascending” means small to large. - Show your working clearly. Markers can follow each step.
Quick Reference
| Skill | Rule | |---|---| | Whole numbers | Compare from the left | | Equal-denominator fractions | Add or subtract numerators; keep the denominator | | Decimals | Line up decimal points | | Ordering | Ascending: small to large; descending: large to small |
Mnemonic: L-D-C = Line up, Decide, Check.
• Line up place values and decimal points. -
compare digits from left to right. - Decide which number is greater or smaller. - Check your answer and operation.
Confidence Check
• I can identify the place value of a digit. [ ] 1 [ ] 2 [ ] 3 [ ] 4 [ ] 5 - I can compare whole numbers. [ ] 1 [ ] 2 [ ] 3 [ ] 4 [ ] 5 - I can order decimals. [ ] 1 [ ] 2 [ ] 3 [ ] 4 [ ] 5 - I can add and subtract fractions with equal denominators. [ ] 1 [ ] 2 [ ] 3 [ ] 4 [ ] 5 - I can check my working for place-value errors. [ ] 1 [ ] 2 [ ] 3 [ ] 4 [ ] 5
Draw five number cards from 0 to 9. Use them to make the largest whole number and the smallest decimal you can.
End of chapter one. 4 more chapters in the full book.
Swipe or use the arrows to turn the page
What's inside: 5 chapters
- 1. Number Systems and Place Value
- 2. Fractions, Ratios, and Percentages
- 3. Algebraic Expressions and Equations
- 4. Geometry: Angles, Lines, and Triangles
- 5. Data Handling: Tables, Charts, and Averages
About this book
"Pre-Technical Studies Notes" is a study guide book by Anonymous with 5 chapters and approximately 3,481 words. Pre-technical studies revision notes and practice questions.
This book was created using Inkfluence AI, an AI-powered book generation platform that helps authors write, design, and publish complete books. It was made with the Study Guide Generator.
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What is "Pre-Technical Studies Notes" about?
Pre-technical studies revision notes and practice questions
How many chapters are in "Pre-Technical Studies Notes"?
The book contains 5 chapters and approximately 3,481 words. Topics covered include Number Systems and Place Value, Fractions, Ratios, and Percentages, Algebraic Expressions and Equations, Geometry: Angles, Lines, and Triangles, and more.
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