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Decimal Expansion of Rational and Irrational Numbers

Write the 2.9...

Question

Write the 2.998 in expanded form

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Solution

$T h e g i v e n d e c i m a l v a l u e i s 2.998 T o w r i t e 2.998 i n e x p a n d e d f o r m, J u s t f o l l o w t h e t h e s e s t e p s : S t e p 1 : T h e s \tan d a r d f o r m o f t h e n u m b e r i s 2.998 S t e p 2 : T h e p l a c e v a l u e o f t h e g i v e n n u m b e r i s 2 - O n e s 9 - T e n t h s 9 - H u n d r e d t h s 8 - t h o u s a n d t h s S t e p 3 : M u l t i p l y t h e g i v e n n u m b e r s b y i t s p l a c e v a l u e . i . e ., 2 \times 1, 9 \times \frac{1}{10}, 9 \times \frac{1}{100}, 8 \times \frac{1}{1000} S t e p 4 : T o g e t t h e e x p a n d e d f o r m a d d a l l a b o v e v a l u e s 2 \times 1 + 9 \times \frac{1}{10} + 9 \times \frac{1}{100} + 8 \times \frac{1}{1000} T h e r e f o r e, t h e e x p a n d e d f o r m i s 2 + \frac{9}{10} + \frac{9}{100} + \frac{8}{1000}$

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