scientific notat

scientific notation and its operations

Week 4

scientific notation and its operations

Glossary

Students will be able to:

Scientific notation: A way of expressing numbers as a product of a decimal number between 1 and 10 and a power of 10.Significant figures: The digits in a number that are considered reliable.Exponent: The power to which a number is raised.Mantissa: The decimal number between 1 and 10 in scientific notation.

i) Define scientific notation and its components.ii) Convert numbers between standard form and scientific notation.iii) Perform arithmetic operations (addition, subtraction, multiplication, and division) with numbers in scientific notation.iv) Apply significant figures correctly in calculations involving scientific notation in real-life problems.v) Understand the importance of scientific notation in various/transcendental scientific fields.

A team of astronomers is designing a new telescope. They need to calculate the optimal size of the telescope's mirror to capture the maximum amount of light from distant stars.Problem:The astronomers know that the area of a circle is calculated using the formula: A = πr², where A is the area, π is a constant approximately equal to 3.14159, and r is the radius of the circle.They have determined that the telescope needs to capture at least 1X10^12 square meters of light.What should be the minimum radius of the telescope's mirror, expressed in scientific notation?

initial problem

example 2 (Changing from Scientific Notation to Decimal Notation)

01. definition

example 1 (Changing from Decimal to Scientific) Notation

Scientists use exponential notation as a compact way of writing very large numbers and very small numbers. A) The nearest star beyond the sun, Proxima Centauri, is approximately 40,000,000,000,000 km away. B) The mass of a hydrogen atom is 0.00000000000000000000000166g. Such numbers are difficult to read and to write, so scientists usually express them in scientific notation

Introduction

Ifapproximate the quotient ab/c

02. Calculating with Scientific Notation(multiplications/divisions)

Use scientific notation, the Laws of Exponents, and a calculator to perform the indicated operations. State your answer to 3 decimal places

exercises

Example

02. Calculating with Scientific Notationsums/substractions

Use scientific notation, the Laws of Exponents, and a calculator to perform the indicated operations. State your answer to 3 decimal places

exercises

04. real-life problems

05. significant figures

The number of significant figures in a result is the number of figures that are known with some degree of reliability

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06. Rounding rules for significant rules

1.- Write the number of significant figures of each of these numbers a)106 b)200 c)0.02 d)1290 e)1209 2.- Write these numbers correct to 1 sfa)280 b)0.072 c)390.8 d)0.001323.- Write these numbers correct to 3 sfa)2971 b)0.3259 c)10410 d)0.50064.- Find the area of a circle with radius r=40.Give your answer to 3 s.f.5.- Find the area of a square with side l= 1.732050. Give your answer correct to 5 significant figures.6.- A car travels 55 km in 1.5 hours. Find the velocity. Give your answer correct to 4 significant figures.

Activity

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