Solve problems that involve exponents and square roots.
Number Framework Stage 8
Most students are intrigued by large numbers. Facts like the amount of money earned last year throughout the world by 5 billion people being about 20 trillion dollars are intriguing. Numbers of this size are hard to read, so a standard form using powers of 10 is preferable.
Using Number Properties
Problem: “What does 10 000 x 100 000 equal? Write it in power notation.”“Explain why 104 x 105 = 109.”
Problem: “How would you work out 1 000 000 x 100 000 000 using powers?”(Answer: 1 000 000 x 100 000 000 = 10 6 x 108 = 1014.)
Problem: “In a programme on TV, a scientist claimed there are 10 billion trillion stars in the universe. Write this amount with zeros and in the power form.
(Answer: 10 billion trillion = 10 000 000 000 x 1 000 000 000 000 = 1010 x 1012 = 1022.) Note: The American system, where 1 billion = 1 thousand million and 1 trillion = 1 thousand billion is used here. The British system, where 1 billion = 1 million million and 1 trillion = 1 million billion, is not used since it breaks the pattern where the names hundreds, tens, and ones are repeated every 3 digits.)
Problem: “A googol is a 1 followed by 100 zeros. Write 1 billion x 10 googols in power form.”
(Answer: 1 billion x 10 googols = 109 x 10101 = 10110.)
Understanding Number Properties:
Complete: = 10 m X 10n = 10? (Answer: 10 m + n)